Your pension is based on your pay so if you move part time, your pay will reduce and so too will the amount of pension you build up from that point onwards. Everything up to that point will be unchanged.
For example if you earned £2000 per month from April to July and then went to £1000 per month from August. For that year you would have £2000*4 + £1000 *8 = £16000 pensionable pay accrued giving a pension (at 1/49th) of £326.53 for that financial year.
In most cases, moving from full time to part time won't affect the final salary part. This is because we use the Full Time Equivalent pay for the final salary calculation, i.e. your basic pay is proportioned up to the same as a full time member. If you have been receiving allowances on top of your basic pay and these have reduced as a consequence of you going part time then this will affect the Full Time Equivalent pay and may result in a decrease in the final salary benefits.
You will now have what is known as concurrent employments - where more than one contract is running and being paid at the same time. A new pension account will be opened for your new contract and will run along side your existing one. The new account is treated separately and will have a new start date.
How this affects your pension depends on how your employer treats the contract. If you have changed your job then generally you will keep the same payroll number and the same contract number for pension purposes. There will be no effect on your pension account as you will just continue to pay in as before. If you have final salary benefits and your hourly rate has reduced then your final salary benefits may be affected by the change.
If your employer has finished off one contract and started up a separate one either under the same payroll number or under a different one then your first pension account will be closed and a new one opened up. These will automatically be joined together after 12 months unless you opt to keep them separate. Options will be sent out to you by the pension team if this is the case.