Nick Clegg has conceded that the new counter-terror bill to be published next week will include a power to force terrorism suspects to relocate to another part of Britain, dropping previous opposition to the measure.

But the Liberal Democrats say they have secured further changes to the existing system of terrorism prevention and investigation measures, known as Tpims, that will make it harder rather than easier for the home secretary to use them to restrict a suspect’s liberty.

The new relocation power will allow the home secretary to require a suspect to live in a particular location in Britain away from their home area – effectively a system of internal exile – as long as there are restrictions on the distance they can be moved and the size of the area within which they are allowed to travel.

The decision by Clegg to drop opposition to relocation powers follows a review by David Anderson QC, the counter-terror laws watchdog, which has concluded that the alternative of establishing exclusion zones around the existing home of a terror suspect would not prevent them meeting harmful associates on their own patch. Anderson had initially proposed the exclusion zones himself.

The new counter-terror bill trailed by David Cameron last week at the G20 summit in Australia will now include a narrower definition of what constitutes “terrorism-related activity” to ensure that Tpims are not used against those whose involvement is peripheral.

The home secretary will also have to satisfy a court of a higher standard of proof than at present before being able to impose a Tpim on a terror suspect. This will be raised from the lower test of “reasonable suspicion” to “the balance of probabilities” civil standard of proof.

The future of Tpims, which replaced the discredited system of control orders under which terror suspects could be put under curfews of up to 16 hours a day, was the last remaining element in the counter-terror package to be introduced next week to tackle the problem of foreign fighters returning from Syria and Iraq.

The package includes exclusion orders which would prevent British citizens returning to the UK for up to two years, powers for the police to seize passports of those leaving Britain, and powers to deny landing rights to an airline that fails to provide its passenger lists in advance.

The runup to the publication of the bill is expected to see a counter-terrorism awareness campaign launched by the police and publication of the long-awaited report by the intelligence and security committee into the murder of drummer Lee Rigby in Woolwich last year.

Ken Macdonald, a Liberal Democrat peer and former director of public prosecutions, said it was important to recognise that measures to protect the public from returning jihadis also had to embrace civil liberties.

“Control orders were a dead end – they didn’t work and we shouldn’t return to them. The counter terrorism bill will command support if it protects security and the rule of law,” he said.

“This may mean allowing the relocation of suspects when it’s really required to protect our people – but only if we legislate to make the test for imposing a Tpim much stricter and the definition of terrorist activity significantly tighter. Proportionate measures like these will serve liberal values, protect our country and deserve public support.”

A Lib Dem spokesman said the Tpims package was a net gain for civil liberties’ and said they had always said they would take a long, hard look at the proposals brought forward by Anderson and that what they had done.

“David Anderson is someone with a history of liberal views and can hardly be described as a tub-thumping securocrat. When he produces a serious report, serious governments need to respond and should do so being led by the evidence,” he said.

“Moving people against their will from one part of the country to another is a significant imposition on their liberty but that is exactly why the Liberal Democrats believe they can only be introduced alongside a higher burden of proof to ensure they are only used where absolutely necessary and in a tiny number of cases.”