Rental income on a work visa?

I have a question that's probably a bit obscure - and was hard to decide where to put it: here, Housing forum, or elsewhere!

I was wondering if anyone here has any experience or knowledge on the legality of earning rental income as a US citizen in the UK on a Tier 2 (General) work visa.

I first came to the UK in as a student and was lucky enough to secure a job and move onto a work visa at the end of my degree. As far as I know the above visa type restricts my income to that obtained through my sponsor/place of work (unless I'm misunderstanding it?).

Ever since I started my job I've been saving to buy a house - and I'm nearly there! However I'm not sure I want to settle long-term where I am now and am worried about losing flexibility. If an opportunity arose in my organisation such that I could transfer closer to my ideal location, I'd like to feel confident that I would be able to let/rent out my home for a few months whilst making the move.

However, I'm not sure if earning rental income on a Tier 2 visa is allowed, hence the question. When I rented down in London, neither of my landlords was British but they were both citizens of the EEA which obviously affords them more privileges than a US citizen on a visa. I was going to ask my visa agent to see what they thought but it being a more obscure question wondered if anyone here might know, and of any sources that might prove helpful?

Thanks very much!

Have you found a bank that is willing to give you a mortgage without ILR?

Our bank, Natwest, would have given me and my husband a mortgage if we had been able to buy. We were approved for the amount we needed to buy the house we wanted. I've only been in the UK for a little over 18 months.

That is you and your UKC partner - the OP implies they are hoping to buy a house by themselves. Totally different. 'We' have also been approved by a bank that would only let the mortgage be in my OH's name, which in essence means that only he was approved.

Ah, I'd read the original and missed that it was the same thread. And for our mortgage, I would have had to be on it for us to have the amount we wanted.