Spouse name must on rental agreement?

[hsmphsmp]

I came to UK in 2008 and rented a house (1BHK) and my wife joined me couple of months later. When the rental agreement was signed, I had only my name on it. When my wife later arrived, I didn't bother to add her in the agreement as I thought it was not necessary.

Now I am applying for my PR, I wanted to get a letter from my letting agent that my wife is living in the house for past 4 & 1/2 years (as proof of cohabitation), they said the rental agreement needs to be checked on the permitted occupants other than the tenant. When I checked the agreement, the permitted occupants section is blank. I am bit worried if letting agent will raise this is as an issue and charge me for it? What is the legal right of my wife when the agreement is made on only on my name. I know it may be a stupid thing to ask, but the way the letting agent questioned made me worried. Can I challenge them if they raise it as an issue and charge me?

Is it must to have both of our names on rental agreement? They charge some 200£ just to do background check before including somebody name on the agreement.

[wpilr_nov12]

Why not wait it out until it's up for renewal?

[hsmphsmp]

It is already running on rolling agreement with 2 months notice on either side, so it won't be renewed. I can end it and start a new one.