You can scarify or rake the lawn to remove the moss.Don't compost it or you'll just spread it round the rest of the garden. Then the lawn needs aerating with a special tool or just a garden fork. The moss will return unless you can solve the problem of the drainage or compaction in the lawn.

Alternatively, wait till April and use a combined Weed, Feed and Mosskiller treatment - then rake out the blackened moss later on and aerate. Aerating again and scarifying in the autumn will help, but if the lawn is in shade for a lot of the year, then moss is inevitable to some extent, and moss is usually prevalent following a drought ridden summer - most of us don't water our lawns, obviously, but this can and does make moss much more likely once autumn arrives.

Thats as I do Bamboo its amazing how quickly it improves after this, but I repeat the feed and weed after 6-8 weeks

Absolutely spot on, Drc - first application in April, and another May/June is exactly right. But no more after that till the following year...

Yes Bamboo I only feed twice each year.