Thanks for all the replies. I removed the saddle earlier and adjusted the two hex bolts that control the gib strip. I gave the bolts a very, very small turn to tighten (Less than 1/16th of a rotation) whilst the carriage was closer to the chuck and it operated nicely i.e. not too stiff and not loose enough to move due to cutting pressure on the tool. It's like this for about two thirds the length of the bed. However the last third of the bed (on the tail stock side) is stiffer again.
The carriage is not engaged on the lead screw when I'm working on the lathe alot of the time, so I don't think that's the cause of the issue but may be worth checking anyway.
It's the wheel on the apron that I am using to move carriage along the bed.
I don't think the wear is bad enough to warrant regrinding the lathe bed just yet…so locking the saddle/carriage sounds like a reasonable solution to maintain a good level of precision.
Does anyone know whether the gip strip itself can cause wear to the underside of the lathe bed? My worry is that a regrind might create a nice flat surface for the top of the lathe bed but the underneath, where the gip strip sits could also wear?