It's nice to see that your test provided with you enough info to find your missing line, minus one ancestor. Quite a lot of us are not that much wiser from these tests, owing to not having close enough matches.
Did you track down all the marriages for all the children of the two couples? And then follow them through the census. Note all the details down, including where they lived. You may find one of them or the parents living with a (grand)child born out of wedlock. From what you've written it seems you find it likely that both your pat-grandfather and his father were born out of wedlock. Based on what you've provided that seems the most likely scenario.
It would be useful if you could provide a spreadsheet showing how much cM those matches share with you, relationship distance, and how they relate to other shared matches. It's not really possible to say much more without all the possible data available. The relationships that Ancestry suggests are just suggestions, they can be something else. So it is possible to make mistakes.
It would also be worth going through matches further to see if you can find matches from previous generations to F1, M1, F2, M2. That will give you firm data that your line is through them, and there is just the a bit of a gap.
It's quite normal to have these gaps and they might never be filled. You might be able to rule some candidates out and consider others more likely. But unless a closer descendant is tested, you will probably have a gap.
It would be worth taking the Y-37 DNA from FamilyTreeDNA ($120, is 20% off periodically). This is a low resolution test that gives you details of matches, and based on that you can see if there are any that are close enough to be worth upgrading to the genealogically useful 700 market test. You may also find from the 37 market test that you have many matches with the same surname as one of your M1 + M2 lines. So you can be fairly certain of what you biological line is. It's also worth noting that the number of Y tests taken by people from the UK is probably no more than 100,000. And many of them are the low resolution tests.
It could really be anything though. I have been through all my lines with a fine comb and its not an exact science. For a long time I thought that apparently not having matches on a line meant there may have been infidelity. But there are many things to consider. One is that there can just be very few matches on a line. Another is matches can get jumbled due to shared ancestry on more than one line. But I have one ancestor born in 1848 who I am sure is not the biological child of either of her parents. But proving lines with each generation get harder. This ancestor could have been switched at birth, adopted, or maybe a previous generation was a NPE. Very often DNA just gives some clues... unless the right match comes along, assuming there is such a person living.
Regarding the suggested 2C match, is there any one line that appears to be in the same area as your line. Also look at each of the matches lines, for the potential (half-)siblings of your ancestor.
Also consider that a likely 2C looks very similar to a half 1C.
