Parliament’s decision to move out of the Palace of Westminster is an opportunity that should be seized; it is also a risk that could be mishandled. MPs voted this week to quit the hallowed Westminster site for at least six years, probably from 2025, to enable major refurbishment of what has become a dangerous and inadequate set of buildings. The plan is to build a temporary replica chamber and to find alternative offices for MPs and peers while the work is carried out.

The cost of the refurbishment and the temporary arrangements is put at £4bn. Yet such figures have a way of rising, especially if contracts are not ruthlessly audited and controlled, as recent scandals have shown. MPs from Theresa May down are understandably anxious that the refurbishment costs could become politically toxic. If the public feels that MPs consider money no object for their own needs while cuts and privations are necessary for everyone else, the already fragile standing of politics risks further damage.

MPs are right to take the decision they made this week. The Palace of Westminster should be refurbished and brought up to modern standards. Parliament’s duty of care to the 7,500 or so people who work there, and the more than one million annual visitors, leaves it little choice. Yet the political risks are self-evident and serious. That is why parliamentarians should also grasp the opportunity to think in radical new ways about how to use the six-year absence for the benefit of British politics more generally.

Resentment of Britain’s elites takes many political forms. The EU referendum was partly a revolt against Westminster. So was the big yes vote in the Scottish referendum. Anger against London and its perceived neglect of Britain beyond the M25 is widespread. The “northern powerhouse” project, to which George Osborne returned in a project launch in Darlington on Thursday, is one attempt to level the national playing field. The north-south divide on skills and education on which the former chancellor spoke is one of many.

Parliament should take this opportunity to reconnect with Britain. If money was no object, it could spend its six years away from Westminster in other British cities – Manchester, York, Birmingham, Glasgow and Cardiff could all make a case, as could others. The transformative effect of cities of culture is well known. Why not cities of politics too? A readiness to reach out might help draw a divided country together. Taking MPs out of their comfort zone might challenge their own prejudices too.

Too ambitious? There are more modest options worth considering. The House of Lords could move, while the Commons stayed in London – or vice versa. Prime minister’s questions could rotate to different cities. The budget could be given in Birmingham or Belfast. Select committees could relocate to new centres. The Commons could sometimes meet in a big top that moves from town to town, county to county.

Parliament will return to a restored Westminster in the end. In the interim, this overcentralised country should think local. Go north. Go west. Be ambitious. Use the imagination. Embrace this richly varied country – and the country may return the favour.