The move comes as China and Hong Kong have said they will no longer recognise the British National Overseas (BNO) passport as a valid travel document from Sunday, Jan. 31.
Britain and China have been arguing for months about what London and Washington say is an attempt to silence dissent in Hong Kong after pro-democracy protests in 2019 and 2020.
The scheme, which was first announced last year, allows those with BNO status to live, study and work in Britain for five years and eventually apply for citizenship.
BNO is a special status created under British law in 1987 that specifically relates to Hong Kong.
China says the West's views on its actions over Hong Kong are clouded by misinformation and an imperial handover.
Anson Law, a 25 year old who works in sales, said he would consider using his BNO status to move to the UK even though the economy there was not as good.
"I's still better than Hong Kong. For example, for young people like us, we don't know how to live or survive here."
Law said people were still monitoring the situation and did not see a large number immediately moving.
Nicholas Muk, a 30 year old teacher who lived in the UK previously, said he would not apply for a BNO visa.
"If people want to move to a foreign country and think the UK is safer than Hong Kong amid a pandemic, that's their own decision."