That is fairly normal for Cyclamen hederifolium at this time of year. Mine look the same. they must have flowered as those round blobs are seed capsules, just waiting for the ants to carry away the seed when they pop open in a few weeks time.

Sorry Amsterdam, but those cyclamen have flowered - profusely. They cannot produce seed heads without having flowered and there are a lot of seed heads in your picture.
If these are current pictures the I would say that you have Cyclamen hederifolium which flowers from August to October. Ours are looking very similar to these at the moment.
The only bit that surprises me is that you say the leaves don't appear until spring, I would have expected them to be visible from autumn.
I would not disturb your large tubers, they look very happy where they are, but lift a few of the seedlings and plant them in a slightly more shaded area.
One final thought, though unlikely, could they be C. persicum that like a hot summer but unlikely to do well outdoors in our British climate.
Written and posted at same time as Owdboggy - morning tea time!

but as said, clearly they flowered hence the seed capsules. are they hidden by other foliage at that time so you don't notice them?

Owdboggy, Bulbaholic and Seaburngirl: - as you said they must have flowered but for the life of me can't remember at all! :0 Good to learn that this is normal as I was about to dig them out and get rid of them. Will take some seedlings and plant in different areas of the garden, thanks for your help on this.