I mean, define heavily.
Compared to a lot of the rest of the UK that wasn't London? Yes.
Compared to London? Not really.
Compared to cities in Germany and Japan? Not even slightly.
We lost about 10% as many civilians to bombing as the Germans did (the UK lost about 40,000 civilians over the entire war, a figure worth noting), and similarly our infrastructure and factories were far less damaged. The Luftwaffe at its worst was as-nothing to the industrial-scale bombing raids of 1944 and 1945. Don't make people with more production capacity than you and who possess similarly amoral attitudes towards civilian populations to you mad, I guess! (Not that it works or achieves any legitimate military goal - bombing civilians is pointless at best, Dan Carlin did a pretty good podcast on that I note).
Growing up in London in the 1980s and 1990s, there were still a few old bomb sites here too. Just places with half-grown-over rubble or waste ground the older people knew had been bombed. By the end of the 1990s or early 2000s I think people hard or were building on pretty much all of them.