The interior of a custom MGB is little different from a stock restoration, save that there are a few additional dress-up options.
A stock interior kit can be had starting around $1600 for good quality. This would include panels, carpet and vinyl seat covers.
Since seats are what connect you to your car, expect to spend some additional money making them right. New foams and diaphragms will add about $100 per seat. Plan on several hours each side to clean up the frames, repair any broken welds and to trim them properly. Leather seat covers will cost around $300 more per pair, and don't forget the rear seat on a GT, which will just about double your seat costs.
Another option are the new seats manufactured by Corbeau specifically for MGBs. They offer improved side support, adjustable recliners, and come in several colors of leather. The frames are made to accept stock MGB runners and are narrow enough to fit the tunnel. These are available from several vendors in the States or directly from the MGOC for about $1400.
A third custom option is to scrounge up a set of Fiero seats. These are one of the few American-sourced seats narrow enough to fit an MGB, and with slight modification will bolt into a B. New covers are available in cloth, vinyl and leather, in several stich patterns. They can also be fitted with speakers inside the headrests.
Seat heaters can be fitted to most any seat, and are a simple addition at the time of retrimming. About $125 per side, plus some minor wiring.
One of the most important additions, I feel, is sound deadening. At the very least, be sure that the factory bitumen-based pads are in good shape on the floorboards. I prefer to add as much modern accousto-dynamic material as the customer is willing to shell out for. A popular brand is DynaMat, but I prefer a product called Accu-Mat. It is available in many thicknesses and compositions for various locations, and can make an amazing difference in removing vibration and road noise. It starts at $30 a sheet and goes upwards from there, but it is one of the best ways to spend money in an interior. Plan on $200-$400 worth of material, plus several hours to apply it properly. Considering the comfort gained, it is a worthy investment.
Completely trimming an MGB interior takes about 2-3 days, depending upon the quality of the kit and whether it is a GT or a roadster.