I believe it's Speedwell. I rather like it but it can spread a bit though not too much.

Agree,most likely one of the speedwells (Veronicas) though can't be sure which one. I have a similar pale blue one which doesn't spread at all (gentionoides) a different one from Arbuthnot's - there are so many.Wonder if it could be spicata either. Whether you should keep it depends totally on whether you like it. I'd keep it if it was mine.

Is it not Purple Toadflax? (Linaria purpurea).

I think so Landgirl...

I'd go for the purple linaria too. its a decent plant and if you like it keep it. it seeds freely and can become a weed when it pops up where you don't want it. but it is easy to pull up.

Bother - I tried really hard to get a closeup of a single flower and the one I chose appeared to be a flat four petalled one. Well my comment still applies - I would keep it and throw out the seedlings that appear where you don't want them. I got mine as a freeby in a clump of something else from a kind Goyer and its certainly romping away!