Generally speaking, settlement agreements can be concluded relatively quickly. If you are happy with the terms of the proposed agreement, your solicitor should be able to finalise the agreement within a few days. In some cases it can even be concluded on the same day. Obviously, if there are further negotiations needed then this will mean that the process takes longer. The timeframe is usually dependant on how quickly your employer responds. Your solicitor will be able to keep you updated on this.
If you have a particularly short or specific deadline, your solicitor will do their best to accommodate this. It is helpful if you let them know the timescales at the start of the process so that they are fully aware.