Ok, we're mad. Saturday we woke up later than intended, had leftover pizza for breakfast and then headed to the station and got the 11:33 train to Kings Lynn and set out from there to cycle to Hunstanton. With no map, and nothing to effect repairs. We found National Cycle Network route 1 and it seemed to be going in the right direction, so we followed it for a bit, and then just followed road signs and our noses. We reached Hunstanton about 2pm or so and went for a potter and a swim and then had fish and chips for "lunch" at about 3.
At this point we should probably have headed back the way we'd come and gone back to Kings Lynn, but we knew there were trains from Sheringham or Cromer, and it didn't look *too* far around the coast, so with the vague thought we could give up and find a B&B at Wells next the Sea if necessary we headed on along the A149, and eventually made it to Cromer. We stopped at the Ship pub in one of the villages (Brancaster: The Ship Inn) for a pint of lime and lemonade (him) or soda (me), and then for an icecream and a sit down at a cafe in Wells, but otherwise just had a couple of little stops for a glug of water, catch our breath, admire the views and to put on lights when it began to get dim. We got into Sheringham at 21:15 and realised we'd missed the previous train by 25 mins, and it was over an hour til the next one, so we pressed on the last 4 miles to Cromer, for a total of 63.5 miles.
To get from Cromer to Cambridge you have to change at Norwich. The last train from Cromer to Norwich is 22:27. The last train from Norwich to Cambridge is 22:10. You can see the flaw with this little plan. So with 45 mins to kill we asked the 4 most immediately obvious places if they had a room for the night, and when they all said no we asked the last for directions to the station, which had entirely eluded us so far. Norwich looked like being almost as hard to find somewhere to sleep in, especially since it was now after 23:00, but the chain hotel near the station pointed us at a street with some B&Bs on it, and one of them turned out to have a spare double room. So for the princely sum of 10 quid each we got a half decent night's kip before getting the first train home on Sunday morning (9:15am), for a very lazy Sunday of dozing, reading, listening to music, takeaway curry and The Truman Show.
Gmap route - though the first bit is rather fudged - the hybrid view doesn't have data at a high enough level to spot off-road routes. The calorie counter on that page is based on running. I've tried entering relevant data into assorted calculators, and it's possibly the trip burned anywhere between about 1500 and 5000 calories.