If your asparagus bed is more than two years old, keep harvesting those delicious spears. Feed the bed with a quality fertilizer, spread a thick layer of compost over it and make sure it is well weeded and you will be ready to go. If you see what looks like elongated ladybugs on your asparagus, kill them off quickly. They are asparagus beetles and can decimate your bed in no time.
Talking of pests, if you see bare stalks of tomato plants, look for large green-striped caterpillars about 3 to 5 inches long. They are tomato hornworms that can be a major pest. You can remove them by hand or, again, spray them with insecticide. Usually, you'll only find two or three on each plant, but each one can remove about a square foot of foliage and nibble into the tomatoes you have been carefully growing.
Feed cabbage, broccoli, brussel sprouts with an all-round fertilizer to keep them growing fast. Feed onions and leeks with a high-nitrogen fertilizer such as dried blood, if you are organic, or lawn fertilizer. Let the rain wash it in.
You might be able to start lettuce and spinach now, but expect it to bolt fast.
In the flower garden
Plant dahlia tubers, gladioli corms, cannas, and other heat loving plants if you haven't already done so. Spray hostas with deer repellent, and keep pruning shears handy for any plants growing where they shouldn't be. Keep after the weeds, and as soon as it stops raining, you might want to tie up roses, clematis and other climbing plants so that they don't sprawl everywhere.
On the lawn
Try to stay off the lawn when it is wet. Walking on a wet lawn compacts the soil making it harder for grass to grow, harder for water to penetrate,
and difficult to fertilize. Having said that, try to keep the grass cut. You'll need to hit your lawn with summer fertilizer soon, so have it ready.
Time to trim the privet if you haven't already started. Keeping privet and forsythia trimmed back makes a good hedge and, if your property abuts a road or path, makes it easier to walk along the path.
Harvest asparagus, chives, oregano, sage, spring onions, and the last of the spinach and lettuce. Oregano and sage can be dried and stored in airtight jars instead of paying a few dollars for commercial herbs. Harvest mint and the first of the basil. If you have a lot, chop it finely and freeze it in ice cube trays.