What is likely to happen is as follows.
The 2-3 weeks you refer to is the consultation period when your job is under threat of redundancy. You continue to be paid normally during this period whilst individual consultations (and collective consultations, if there is a union involved in collective bargaining).
One is not actually redundant until one has a latter to say that the redundancy will occur as of XYZ date.
The company has two choices - it will either demand that one works out one's notice period, then at the end of that period one gets whatever redundancy money is due - minimum of stautory levels of reduandancy payments or enhanced - depends on what was agreed.
Alternatively one gets a sum of money at date XYZ and one leaves immediatly - and that total sum of money includes money in lieu of notice PLUS the redundancy money.
In this latter situation, one has actually left the employer at date XYZ, even though one has been given extra money in lieu of notice. In THIS situation it is perfectly OK to start another job just as soon as one can find one.