The first thing to say, given that you say "I have just a few days to apply for ILR" is that it is essential that you submit the application for ILR
before the expiry of your current 2-year spouse visa.
OK, the Tax Credits question! It does not surprise me at all that Croydon continue to get it wrong, as regards this rather technical matter. So lets just set the scene. Firstly, you have child(ren)? If so it is essential that the Child Benefit claim is made by your British Citizen spouse, and certainly not by you with the "No recourse to Public Funds" restriction on your visa.
Tax Credits? For a couple living together it is absolutely necessary for a Tax Credits claim to be made jointly by the couple. It would be very wrong for the claim to be made by just one of a couple. At first glance the "No recourse to Public Funds" restriction on your visa causes a problem. However some "small print" in the Tax Credits legislation is extremely useful to you and your spouse. Namely reg 3(2), Tax Credits (Immigration) Regulations 2003 says that where a couple consists of one person who is not subject to immigration control ... your spouse ... and one person who is subject to immigration control ... you .... then
for Tax Credits purposes only they are both treated as being not subject to immigration control ... and hence a claim to Tax Credits is totally OK for such a couple.
Reg 3(2) is reinforced in its application by para 6B of the Immigration Rules :-
6B. A person shall not be regarded as having recourse to public funds if he is a person who is not excluded from specified benefits under section 115 of the Immigration and Asylum Act 1999 by virtue of regulations made under sub-sections (3) and (4) of that section or section 42 of the Tax Credits Act 2002.
-: and i confirm that the regulations, that is, the Tax Credits (Immigration) Regulations 2003, were indeed made under section 42 of the Tax Credits Act 2002. So clearly, in your circumstances, you are "not be regarded as having recourse to public funds" .... but don't be surprised that the Croydon so-called Helpline continue to get this wrong. The detailed legislation is there to support you.
It matters not at all that it is you working, and your British spouse not working .... that is simply not an issue here.