A second job does NOT in itself mean higher rate tax. You only ultimately pay higher rate tax if your taxable earnings in total breach the 40% band (currently �34,800, meaning effectively total wages of �40k).
However, it is not possible to split your tax allowances between two jobs so, presuming you take them all in the higher paying job, the second one will see you pay tax initially at basic rate (ie without an exempt band). If you earn more than the basic tax allowance of �6,035 in job one it ultimately won't make any difference. If you don't then you'll overpay tax initially but get it back at the year end.
Fundamentally though your second job will be taxed at 20% flat rate (no allowances). NIC will of course still be payable if you earn over �105 a week.