A decade+ ago Hull Trains did plan such a service routing from Cleethorpes, Lincoln, Sleaford, Spalding and Peterborough. The reason given for not starting then was they didn`t want to start a service whilst work was ongoing on the Joint line but preferred to wait until it was all finished. Not sure what happened there ?
By the time the work has been done, the DfT had blocked off the paths from Peterborough with the TL timetable and the Lincoln via Newark service was on the cards.
The HT plan (actually done by GB Railways) was to go Grimsby, Market Rasen, Lincoln, Sleaford, Donington, Spalding, Peterborough, Huntingdon, Kings Cross with Stevenage as an option if it could be done.
Market Rasen was for Louth via the A361 and a reopened Donington Road (which was then a lorry park) was for Boston, being situated directly on the A52. An option for early first and late last trains of the day starting from/ finishing at Boston was also considered.
Fitting batteries to some TL units would allow for a similar service in future - at least as far as Lincoln, if someone ever wanted to do it.