The rules are due to end in March – but that could be brought forward if “encouraging trends continue”.
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Boris Johnson has said he plans to end all remaining Covid restrictions in England – including the legal rule to self-isolate – a month early.
Under the current rules, anyone who tests positive must self-isolate for at least five days.
The current restrictions are due to expire on 24 March.
But Mr Johnson told MPs he expected the last domestic rules would end early “provided the current encouraging trends in the data continue”.
He said he intended to return after parliamentary recess – which is from 21 February – to outline the government’s strategy for living with Covid.
At the start of Prime Minister’s Questions, Mr Johnson said: “It is my intention to return on the first day after the half-term recess to present our strategy for living with Covid.
“Provided the current encouraging trends in the data continue, it is my expectation that we will be able to end the last domestic restrictions – including the legal requirement to self-isolate if you test positive – a full month early.”
Cases have been falling in the UK since the peak in early January.
Latest daily official figures for the UK on Tuesday showed another 66,183 people tested positive for Covid and a further 314 people had died. There are currently 1,421 people in hospital with Covid.
And about 85% of people over 12 have been vaccinated with at least two doses.
Rules for travellers coming to the UK are also being relaxed later this month.
From 11 February fully vaccinated people coming to the UK will not need to take any Covid tests. Travellers who are not fully vaccinated will no longer have to isolate but they will have to take tests.
The rules on self-isolation differ across the four nations of the UK.
In England – like in Northern Ireland – anyone who develops symptoms or tests positive for Covid via a PCR or lateral flow test (LFT) must immediately self-isolate.
People are able to leave quarantine after five full days if they have two negative LFT results, 24 hours apart.
In Scotland and Wales, people must self-isolate for at least seven days – as soon as symptoms appear or they test positive.