Your tenant gambled that you would let them break the terms of the lease.  

You have to do the math regarding what it's worth to keep a known hassle-free tenant vs gambling on a new one.  

And maybe some tenants who can't find the type of unit you are offering in that particular area, so they're willing to gamble you'll get the work done on time, and that it will be done right.But, even then, I think you'll be renting to people who will be coming into the rental with an eye that is looking for problems and things to complain about.  

Really, I have to agree with Greg on this one, as far as it being easy to deny them, and from my personal experience, it's worth the gamble.  

You could check on a UK credit record, but I really see no point.As for criminal records, as part of the visa requirements he would have got an ACPO certificate (think that's the right four letters) which is a certificate from Hampshire Constabularly iirc who do a background check within the UK.

It's a gamble IMO and goes against the notion that you should make your money in real estate when you buy. 

I prefer SFRs with no HOA too ... higher buy in cost, but generally better appreciation & tenant class, more control, more "value add" possibilities (try doing an addition on a condo :)), and no unpredictable HOA fees or assessments to eat into my cash flow.So, though some think that all that buy RE in CA for appreciation are crazy gamblers, and many in fact are, I myself am incredibly conservative, because of my multiple exit strategies believe that what I am doing is NOT gambling, and have the consistent long term track record of profits (in BOTH appreciation AND long term cash flow) to back it up.

Some people are more into gambling than others, that's all.

The issue is that I would gamble they will not pay via money order to your P.O.

You can put whatever you like in your contract, but if it falls under the category of what the law deems to be an Unfair Term it will not be legally enforceable.This is the  UK publication entitled Unfair Terms in Tenancy Agreements.https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/284440/oft356.pdfHere's what it says about forcing your tenant to buy renters insurance.unnecessary insurance requirements - we consider that whether tenants wish to insure their own personal belongings is a matter for them and that it is unreasonable for the landlord to make this a contractual requirement.