Very possible. In Great Britain the population density is one of the highest for any country in the world. In terms of density the UK, which is GB + Northern Ireland, comes in 53rd whereas the USA is 179th about 7.5 times less dense.

It has a well developed commuter rail and bus system. Most commuters in the London area for example would commute in by train. For longer journeys most places can be reached by rail or coach. You can travel direct London to Paris by rail via the channel tunnel.