This seems perfectly consistent. What I've learnt is that matches are very much down to probabilities and randomness. I read somewhere for example, that an actual 4th cousin only has about a 50% chance of showing as a match.
Also, two 3rd cousins who are descended from the same ancestor, will both have dna from that ancestor, but have got different parts with no overlap and hence don't show as a match to each other. I think this is what is happening in the case you describe.
I have some reasonably high cM matches who, when I worked out the connection, were much further back in time than I was expecting. It seems that sometimes large segments are passed down a long way by chance.
Personally, I would work on the common people in the trees and start looking for siblings/aunts/uncles and then start working downwards. You might get lucky and there is someone who moved to Leicestershire or find some links that would be worth investigating.
You said the 220 and the 59 both have the same people in their tree. How many generations is each back to their common ancestor? 220 is a high match and I would guess that your friends grandparent and the 220 matches grandparent could be siblings (other relationships are obviously possible; ancestry gives you the percentages for the different possible relationships but this one is a good working hypothesis).
Hope this helps (but I'm not an expert, just observations from my own search).