If you elect to be covered under the
US-UK Totalization Agreement, both you and your employer will pay US Social Security and Medicare taxes at the usual rates on your UK salary. Alternatively, you and your employer can both pay UK National Insurance contributions instead. In either case, your employer must take the applicable social security taxes out of each paycheck, just like now. This would only change if you were self employed.
On balance you will probably find the UK (particularly the southeast) more expensive than the US, particularly if you are coming from a relatively low cost location in the US, but some aspects of living in the UK can work out much less expensive. The single biggest whack is probably the higher rates of UK income tax, although this is offset by usually having no state income tax to pay.
If your wife is a Tier 2 dependant, she can work. In fact her entitlement to work will be considerably more generous than yours, since you must work for your Tier 2 sponsor but she can work for any employer.