I am going to try out a recipe I found in a magazine earlier this month. The recipe calls for Muntons light LME and Muntons light DME. My online homebrew supply shop I usually use does not have Muntons but another brand. (Briess I think). How dependent are recipes on the specific type of LME or DME that I use?
You should be fine using whatever brand you find of DME and LME.
I usually just use generic liquid extract and what brand of DME that the homebrew shop has. I often use Briess.
There is one minor caveat, however, with respect to substituting brands of liquid malt extract and that is beware of substituting brands of pre-hopped malt extracts.
Substituting brands of hopped extract tends to be problematic since rarely do such extracts give any indication as to the hopping rate and/or IBUs.
If you know the IBU value then you can always use additional hops or dilute with more water if necessary. Without such information substituting brands of pre-hopped extract is pretty much a gamble.
For this reason I never use hopped extracts. I suspect you are dealing with unhopped extracts so you should be fine.