My guess would be a clouded funnel cap (Clitocybe nebularis) unfortunately you've cut the stem thereby denying us the identifying feature of a bulb at the stems base. For identification purposes please always pull the whole of the stem up as the stem base shape is important, you mentioned they were growing in rings which is useful but the other thing needed is the habitat they were found in as most species only grow in a specific place such as under beach trees or in open grass land etc.

I suggest you go to Rogers Mushrooms | Mushroom Pictures & Mushroom Reference
and Fungi Britain Europe identification guide scientific names