No pay rise until agreement to increased notice period?

[Quangoquandry]

All, lookimg for some guidance here please. I've been "promoted" (band change) so I am fairly compensated for a role I have been doing for two years.
Letter received states my new salary and notice period is 3 months (previously 1) and I am to sign to confirm I am satisfied. The hitch is that payroll won't be updated until I sign and return letter. Can they withhold my increased salary until I sign?
The reason I ask is I am hoping to move jobs (1 interview down) but don't think the process will be complete that quickly. Tia

Standard for the NHS - if you look at the employee handbook, standard terms and conditions alongside each band. I think up to band 4 is 4 weeks, bands 5- 7 is 8 weeks, 8a - 8c is 12 weeks and I think up to 6 months for 8d and esm (please do not quote me!)

Since you've said band i am presuming this is NHS, in which case it's not that they are raising your salary, it is that they have agreed to re-band your current role to a higher band. In which case, you have to agree to all of the T&C stuff applicable to the new band - Ie a longer notice period.
So if you want the higher paycheck, you need the higher band, so you need to accept the longer notice period. They wouldn't be "withholding" anything as if you don't sign and return you haven't accepted the higher band, so you'll stay at current band and salary until you do.

If you're negotiating a new position somewhere else, you could state your 'new' salary as a baseline, while not actually signing up to the new contract if you will be leaving anyway.