Not sure exactly how long - your US credit will mean nothing in the UK, so you will be starting from scratch to build credit.
In terms of qualifying for mortgages, I think some people have had difficulty qualifying for a mortgage before they had ILR (permanent residence). What type of work visa will your wife have? If she is on a Tier 2 General visa (she is being sponsored by a UK company that she has not worked for before) it will be 5 years before you can qualify for ILR, but if she is on a Tier 2 Intra-Company Transfer visa (she is being transferred to a UK branch of her US company), it doesn't lead to permanent residence, so you won't be able to qualify for ILR at all on that visa.