There are loads of Shelters/adoption centres that have open days, they are the centres that are HQ sponsored and have some paid staff and are usually much bigger than the branches and have all the cats in one place. If you go to www. cats.org.uk then home a cat, then find your nearest CP, a map of the UK will come up, if you click on your area there will be 3 options 1) Shelters/adoption centres. 2) Branches, some of these will also have open days but due to the fact that all Branches are manned by unpaid slaves volunteers they often don't have the capacity or environment (as usually it is private homes that are used for fostering to have open days. 3) shops.
Of course the National Cat centre at Haywoods Heath is really the best place to go as it is where The CP HQ is and also an adoption centre with I understand up to 200 cats, it cost hundreds of thousands of pounds and has every facility you can think of.
Everyone that sponsors cat cabins is invited to open days as a matter of courtesy but of course everyone is more than welcome.