You would have two options. Your company can still employ you directly, but they would need to provide you with a UK contract. You could still be paid in USD, through US payroll, into your US account. But things like paternity leave, minimum of 28 days holiday a year, etc., would need to be in your UK contract to be legal. Or you could be a self-employed contractor and bill them accordingly (hourly or day rate).
No matter what option you choose, you would pay UK taxes (it's where you are a resident, not where you are being paid from). You would then file for a Foreign Earned Income Exclusion with the IRS to not be subject to double taxation. UK taxes are higher than US taxes so that is something to consider when negotiating with your current employer.
Also keep in mind that if your wife is coming on a Tier 2 Intracompany transfer that the visa does NOT lead to settlement, meaning your move would be temporary. It's just good to know going in. Only Tier 2 General can lead to settlement.