According to M&J's link they will still need to pay stamp duty on both properties.
The good news is that mortage valuers are routinely under valueing property at the moment so you can use the lowest estimate of value that you get as the dutyable value. The taxman is unlikely to question a written valuation from a professional valuer/surveyor.
No, you can't do it. The Inland Revenue (who run Stamp Duty) call this a "linked transaction" and you have to declare on the return made to them whether or not this is the case.
Don't risk it, the penalties (interest, fines and possible criminal action) are just too risky and it could be years before they come after you. Do you want to have the possiblilty of this hanging over you?
Also, if you are buying with a mortgage your solicitor has a duty to tell you lender if you are buying at an undervalue and explain why. Your lender may (a) not lend at all because they will know it's dodgy or (b) lend you a hugely reduced sum based on the price you are paying, rather than the value.