What is the cheapest way to replace them?

 

Myrtle Ltd sells replacement kits; although I wouldn't exactly call them cheap.

https://www.myrtleltd.com/product-ca...r-daimler/xjs/

 

That would depend on how bad your existing wood is, how much work you want to do, and whether or not you want to keep it stock.
It's not expensive to strip and re-veneer the panels. Just a lot of work and does require some woodworking and finishing skills.
The easiest is to "wrap" them. This will give you some idea what's available. https://www.ebay.com/i/192552548086?chn=ps
I did my '93 coupe wood trim in carbon fiber wrap. Easy to do but definitely not for the purists!

 

Years ago on an extremely budget restrictive project I sanded all the old veneer away, clamped & glued new veneer onto the wood pieces, stained the veneer, and then covered it with this stuff:

https://www.michaels.com/envirotex-lite-pour-on-high-gloss-finish-8oz/10178984.html?cm_mmc=PLASearch-_-google-_-MICH_National_PLA_Shopping_Null_Null_Tier+1_Genera l-_-All+Tier+1+Products&&cm_mmc=PLASearch-_-google-_-MICH_National_PLA_Shopping_Null_Null_Tier+1_Genera l-_-All+Tier+1+Products&gclid=CjwKCAiArK_fBRABEiwA0gOO czagM--iikLxOmdpwhv2foHfiJkobNvJux9Z5zG4bA8UBmtpEMPoSRoCq f8QAvD_BwE&gclsrc=aw.ds

It pours on and is self leveling. Turned out pretty good. Wasn't a huge fan of the veneer I chose or the color I stained it, but it was proof of concept that it can be done. AND it only cost about $40 in supplies



Then, a couple years later I gave it a shot on my dad's project car's ski slope. Chipped and sanded it down to bare metal, reveneered and used the same EnviroTex stuff. Second attempt was even more successful; mostly because I chose a veneer that more closely matched the original and stained the wood the right color. (Note I only did the ski slope in these pictures)




Bottom line is with a little skill and a lot of clamps, it CAN be done! (The taxi driver handle on the steering wheel was his solution to the power steering being out lol)