Ground cover

I wanted to try to keep the weeds down in the corner of the front garden under the flowering cherry so I've planted some ground-cover plants there last year and earlier this year. 
This one was put in last but it's smothered the others now and is taking over that corner. It's great for keeping the weeds down but I think it might be at the loss of some of the other ground-cover plants. It's a nice plant but it's not nice enough to let it to smother the rest! I will chop it back soon and if it doesn't behave I might have to dig it up.
I was thinking it would make a nice lawn - it's like a cushion and very green. I am pretty sure it's thyme but its label is missing or it's engulfed it!
Not done much today other than pegging washing out and little bits of household chores. Bit of a lazy Sunday.