Covid-19, why didn't the UK stop people leaving the country once the new covid variant appeared?

It is more transmissible.  It is not GIGANTICALLY ASTRONOMICALLY more transmissible.

Without social distance and masking, non UK variant:

If 6 people had covid, 4 of them would give it to 5 people and 2 of them would give it to 6 people. (each person would give it to 5.7 people).

= 32 total

With the UK variant:

If 6 people had covid, 5 of them would give it 6 people and 1 of them would give them to 7 people. (each person would give it to 6.1 people).

= 37 total

But since most people social distance and mask:

Neither 32 or 37 people would have gotten

In real life 5 people will give it to 1 or 2 and one will give it to 8.