From what I can see of the bee picture, its probably andrena haemorrhoa - this is a mining bee, its solitary, although other females may also be nesting nearby. They like very sandy ground, and they lay only one or two eggs each season, and then disappear. This is the time of year you will notice them in lawns or paths, etc. Very valuable pollinator, falling population like most bees, unlikely to sting, suggest you just wait for them to leave. Sometimes females are still around as late as June, but usually gone by end of May.
Your lawn looks as if it needs a fair bit of maintenance - suggest you scarify thoroughly in autumn and apply a treatment such as Autumn toplawn. Apply feed treatment to the lawn in the growing season (Lawn Weed and Feed with or without mosskiller), but wait till June as the bees are present. They probably seem like a big nuisance, but they're very important creatures and beneficial to your garden.

Thank you Bamboo for your reply and good advice about the state of our lawn!! I've posted another photo of the insect - there are at least 2 around at the moment and there have been others previously. Just to put you in the picture, we live on the west coast of Scotland about 35 miles south west of Glasgow.

Google andrena haemorrhoa and compare what you see there with what you've seen in your garden...

i doubt very much they are actualy hurting your lawn anyway .