Is it possible to buy a return ticket which allows me to go outbound via Peterborough and return via London?
I would like to take the 16:17 outbound on Saturday and then return Sunday morning.
1 Adult 1 Child with F&F railcard.
The best I can find online is 2 single tickets for £150.
This is one of the circumstances where you are likely to be overcharged when buying online, as online retailers cannot issue excesses.
If you're only interested in walk-up through fares, then the cheapest option will be to buy a 'not via London' Off-Peak Return (£66.85 for you with the Railcard, £19.20 for the child) and then to excess the return portion to '+via London'. As you are only excessing one portion, you should be charged half the difference - which should be £4.75 + £1.40 = £6.15. So the total cost should be £92.20.
Is there a particular reason you want to return via London? If you're prepared to return avoiding London, you can do the whole journey for a lot less, even with walk-up tickets. Splitting at Leicester and Peterborough, the fare would be £64.45 total. Or as little as £53.80 on Advance tickets (the ideal split points depend on exactly which itinerary you take).
If you go for the excess option, whilst you're perfectly entitled to pay the excess onboard the train (without penalty), not all staff have the required equipment or training to issue excesses or cross-London tickets. So you may prefer to obtain your excess at a ticket office prior to making your return journey, to avoid any hassle e.g. crossing London. You can get the excess at any ticket office; it doesn't have to be the same place you originally bought your tickets.