Assuming that you'll be returning on the same day, you can catch the 0749 train from Attleborough to Ely, arriving at 0827. Then take the 0845 train from Ely to Kings Cross, arriving into Kings Cross at 1004. The regular Off-Peak Return fare is available on that train for £52.80. (It's a 'walk-up' fare, so there's no need to book in advance).
Using an Off-Peak ticket will mean though that you will need to commence your return journey from Kings Cross no later than 1612 OR from 1912 onwards. (Using peak-time services would cost you a whopping £119.10).
If you're only going to Green Park (and not then onto other places in London), the cheapest way to add on the bit between Kings Cross and Green Park is simply to use a contactless debit card for your Tube journeys. (£2.70 outbound. Either £2.70 or £2.80 for the return journey, depending upon whether or not it commences between 1600 and 1900).
If you'll be touring around central London though, it might be better to buy an Off-Peak Travelcard at Attleborough for £60.40. (Although it's called 'Off-Peak', it can still be used without extra charge between 1600 and 1900 on the Tube).
There aren't any 'Advance' tickets available from Attleborough to London when you want to travel. If I can find any available by splitting your journey at Ely or Cambridge, I'll post again.