If there is a genuine accord developing between the Conservative and Liberal Democrat officials thrown together at the heart of the coalition for 100 days now, it is one forged as much over shared drinks in Whitehall pubs as inside shared offices.

Some Tories inside Downing Street rate new Lib Dem colleagues on "pintability", while a mass outing to a local watering hole on the last Thursday of the parliamentary term was intended to encourage the rare shrinking violets not already mixing with their former political foes.

Over these drinks both sides are discovering that while ideological differences undoubtedly remain, they are not as wide as many expected. "The Tory staffers inside Downing Street are on the left of their party," said one Lib Dem. "And of us lot inside Downing Street, we're on the right of the party. So there's not much between us." There may not be much between them, but faultlines are opening up nonetheless.

Walk through numbers 10, 11 and 12 Downing Street and sure enough there are countless little tableaux of a living, breathing, hybrid government – teams composed of both sides who only return to their respective home sides for morning and afternoon meetings with David Cameron or Nick Clegg.

At the building's heart, a sharp left before the cabinet room, is where Cameron and Clegg's principal strategists, Steve Hilton and Polly Mackenzie, engage in "horizon scanning", developing a longer-term, shared narrative where there is currently an impasse, for example social care or public sector pay. Clegg is based in an adjacent building to No 10 and Mackenzie is his eyes and ears inside Downing Street. The 29-year-old delayed her wedding to her film producer boyfriend after it collided with the clearly unexpected entrance of her party into government.

Overlooking the Downing Street garden, Hilton and Mackenzie sit opposite each other in an informal atmosphere. The sometimes shoeless Tory svengali sets the tone for the retro T-shirts and denim in his policy team.

Back on the central Downing Street corridor is Cameron's private office, run by chief of staff Ed Llewellyn. This is the calmest part of No 10, run in what civil servants describe as "the style of John Major", with the prime minister's red box closing to official papers strictly at 6pm every day. On the left is the office given to those doing the more day-to-day policy work of these first 100 days, Conservative Rohan Silva and his Lib Dem counterpart, James McGrory. At first glance, both just resemble football supporters nearing the end of their 20s, but there are also supreme levels of political wonkery at play. In the same room are former civil servant Paul Brown and Tim Chatwin, respectively the government and political appointees in charge of running the all-important "news grid". This room is all about short-term policy and planning: policies come through here, go to Cameron and Clegg and then, when approved, are despatched to far-flung corners of Whitehall. On a floor above sits Tory James O'Shaughnessy, one of several officials who looks like he should be running a record shop. As head of the policy unit he is in charge of the awkwardly-named "structural reform plans" ‑ making sure departments are reformed to implement ideas in the coalition agreement, something for which ministers have to file monthly reports.

Once policies are formulated, they must be packaged and spun. This happens along the corridor into No 12, masterminded by Andy Coulson, Cameron's head of communications. He and fellow Tories Henry Macrory and Gabby Bertin have spent the last three months working alongside Lib Dems Jonny Oates and Sean Kemp. This, says one civil servant, is "the most political operation Downing Street has ever had".

Complex and carefully balanced as this policy operation might be, in power terms it is a sideshow to the main coalition event: the Treasury, and its key ministers. Regular Downing Street visitors describe a quartet at the heart of government: chancellor George Osborne, his Treasury No 2, the Lib Dems' Danny Alexander, and Cameron and Clegg. Osborne has developed a relationship with Clegg so the four can work as a team. They went through Osborne's budget, line by line, on their own in the cabinet room. The same four are now liaising ahead of the comprehensive spending review on 20 October.

In some ways what is most remarkable as the first 100 days come to an end is how Downing Street has eased its control over Whitehall, only to find the Treasury taking up the slack. In some spending negotiations, the Treasury has gone right down to the £10,000 mark.

Osborne and Alexander have roles in looking over the policy proposals of the Hiltons, Mackenzies and O'Shaugnessies of Downing Street, with Oliver Letwin, minister of state for policy, another key fulcrum. Policy from Silva and McGrory's team is said to pass through Hilton's hands before going to Osborne, then "Danny and Oliver oil the wheels", before something is emailed to Cameron and Clegg. After this it may get passed to one of the many sub-committees that Clegg chairs and then, if there are substantial changes, back through the system again.

One of the many curiosities is that while some friendships blossom across the divide – Alexander asked a Tory aide, Ramesh Chhaabra, to handle his media, Ken Clarke and Tom McNally have become firm friends at the justice ministry – the first of the two faultlines cracking is within the Tory party.

A key problem for the Tories, say civil servants spectating and taking part, is that Coulson doesn't talk to Hilton, and so press is cut off from policy.

Recently it was reported that the government was considering an end to free milk for the under-fives. Just before a BBC interview on the Sunday morning, the Tories' education minister, David Willetts, checked with Downing Street's press minders before defending the plan – only to learn, on air, that it had been reversed.

Had the press team been talking to the policy team, insiders say, they would have known the policy had been considered and rejected four days earlier. Osborne comes the nearest to bridging this divide as the only one to talk to both Coulson and Hilton during his many daily trips into Downing Street from the Treasury. Reinforcing the clout of the Treasury by dint of his social skills, Osborne, says one civil servant, is the "rock" of this government.

There are also worries within the Lib Dems, particularly given Clegg's plunging popularity ratings. Some argue that he is clearly missing his former chief of staff, Alexander. Clegg tells friends that Alexander has "disappeared" into the Treasury and he barely sees him these days. Civil servants are damning about Clegg's private office. "Frankly dysfunctional," said one. "Shambolic," was another's verdict.

Clegg tries to keep on top of everything that appears on Cameron's desk, and when he left for his summer holiday in Spain earlier this month he was clearly "frazzled". The party's operatives at the heart of government appear unclear how they can use civil servants to their own ends, whereas the Tories have a better feel for this, others say. The Lib Dems are said to be retreating into their own clique, and closing ranks within Downing Street. Mackenzie is well-liked, but she has the job of scanning all government policy for Lib Dem elephant traps. She cannot physically keep up.

There are many inevitable tensions from trying to force some notably varied policy ideas into the coalition's one-size-fits-all narrative. Hilton sits in meetings and asks of all suggestions put forward: "But is it transformative?", while his hand indicates thought-bubbles ascending from his head.

With a problematic split between Coulson and Hilton and, separately, Clegg feeling out on a limb, honest brokers in the two parties won't report that they have yet completed the transformation of Downing Street.