This depends on the terms of your settlement. It is normal for payment of your salary to be paid as normal until your employment ends. Then the lump sum (often called a termination payment) is normally paid after your employment has ended but how quickly this happens depends on the terms of the settlement agreement. Typical periods can be anything up to 28 days but often around 14 days. The timescale is normally from when the employer or their representative receives the signed agreement or the date your employment terminates whichever is later. It can take longer to process the payments from large employers.
If this causes particular hardship or is abnormally long then it is possible to request as a point of negotiation that this be brought forward with other amendments to the settlement agreement. It is important to remember that the agreement is not binding until it is signed so until that happens there is still a level of uncertainty. I have only come across a couple of examples where the employee has not been paid as contractually set out in a settlement agreement. It is important to remember that your employer may avoid having to pay you if you are in breach of contract so it is important that you stick to your terms of the agreement particularly the warranties and returning company property for example as this can cause delays or bigger issues.
It is rare for non-payment to occur but it can be a case that the payment may be late particularly in larger organisations where the action date is some way in the future so sometimes it is necessary to chase the payment. In the unlikely event that you do not get paid and you have a valid agreement the correct forum for the dispute would not be employment tribunal as you have signed away your rights to bring those claims but for a claim to enforce the agreement which would be in the county court like other contractual claims. If this should happen you will need to take advice and the starting point would be the solicitor who advised you on the agreement. Don’t worry this is rare.