Regularly mow lawns to keep them in shape - removing 'little and often' is the key to a good quality sward. Continue cutting lawn edges with a half-moon edging iron to ensure they are neat.
Mow pathways through areas of long grass to allow access to other areas of the garden.
Add grass clippings to the compost heap in thin layers (too much grass all at once is likely to be very wet and poorly aerated, resulting in smelly slime rather than compost).
Apply a high nitrogen summer lawn fertiliser if not done last month to encourage a healthy-looking lawn.
Move garden furniture and other objects regularly to allow grass to recover and prevent yellow patches.
Ensure new lawns (either from turf or seed) do not dry out during hot weather, as turves will shrink if allowed to dry out, and fail to knit together.
Troubleshooting
During periods of prolonged dry weather, you could help by keeping your lawn a little longer than usual, and even investing in a mulching mower. Mulching mowers shred the grass clippings very finely and then blow them into the lower layers of the turf, where they act like mulch to help the lawn retain moisture. Because the clippings are fine, the end result is not unsightly, especially later in the season when the lawn gets very dry, and the mulch helps to keep it green rather than brown.
If moss is a problem, choose a combined fertiliser and mosskiller when feeding the lawn.
Selective weedkillers are available for lawns, which will kill the weeds but not the grass or any naturalised bulbs (providing they've died down). However, they will kill wild flowers.
Disperse dry worm casts with a hard-bristled broom.
Molehills can be a problem in rural areas. Traps are the most effective way to deal with this problem.