Will I face issues getting a re-entry permit for Thailand if I travel during my 60-day Covid extension?

>If that's during the Covid extension, will I have a problem getting a re-entry permit or relying on it when I return to Thailand?

A re-entry permit keeps your current extension of stay "alive". *IN THEORY* you should be able to get an re-entry permit to keep your current 60 day extension of stay based on unable to travel due to COVID-19 alive. The re-entry permit is 1,000 THB. However, since a 60 day extension of stay based on unable to travel due to COVID-19 is because you can't travel back home, there's a chance that they would not sell you the re-entry permit, or (a slim chance) is that you'd get rejected at the airport.

A much much better option that's only slightly more expensive would be to get another single entry Non-O visa based on marriage to a Thai national. This would give you 89 days on entry. After you return from the UK, your money should be seasoned for 2 months, and you can apply for a one year extension of stay based on marriage to a Thai national when you have 30 days or less remaining on your current entry stamp (45 days at some immigration offices).

A single entry Non-O visa based on marriage to a Thai national is 2K THB in local currency :)