We need to understand whether your employer has given you written notice of redundancy (i.e. the consultation period has completed and you have definitely been selected) or whether the consultation process is still in progress covering a number of employees (i.e. you are one of those in a pool selected for potential redundancy).
Assuming it is the former, and you have a letter setting out your termination date and the make-up of the redundancy payments due to you at termination date, then I suggest that, if you want to leave earlier, you talk to your employer. Do not disclose that you have another job - just say you want time off as a break.
You may be able to negotiate an earlier leaving date with the balance of your notice money paid as 'money in lieu of notice'. There is no obligation for your employer to grant this, but some will. There is a financial incentive on both sides to do this, as the employer is not liable for employer's NI on payments made in lieu of notice (13% of salary), nor company pension contributions, so it saves them money. It saves you money too as, not only do you avoid paying the employee's NI on the lump sum, but it becomes part of the redundancy lump payment and hence is not liable to personal income tax (if below a maximum figure).
I stress though that there is no obligation on an employer to release you early, if you are considered to be needed right to the bitter end.