Taxis are usually available at Newark Northgate for most of the day. There is a rank within the station forecourt (only for taxis who pay the fee for access) and another on the road outside (just to the right when leaving the station).26/7 travelling fr Stansted to Lincoln. Are there always taxis at Newark NG to go to Newark Castle. Not capable of that walk.
Thank is very good advice and something I hadn't favored into my replyPlease consider ticket type before looking at alternative routings (e.g. via Peterborough) as Advance tickets may require the OP to stick to a specific service from Peterborough to Newark North Gate.
If you have open tickets (Off Peak/Anytime), then I'd look at alternatives, if they're Advance tickets, you need to travel via Newark.