If you still have sufficient holiday days remaining in your adjusted yearly entitlement, then you are entitled to take the time off as originally planned and it would not count against your notice period. Four weeks notice would still be 4 weeks notice, your leaving date would not change.
However - because you're leaving the company mid-way through the year, any holiday entitlement you may get, will be adjusted down on a pro-rata basis. The amount depends on your total entitlement for the year (not including public holidays), so if you get 25 days for the year (as an example), you would accrue approx 2.1 holiday days per month from the start of the holiday year in your organisation. Note: this isn't always January to December, but will be defined within your organisation somewhere, possibly within your employee handbook, if you have one.
So if your holiday year runs from Jan to December, you would accrue 2.1 x 8 (months - Jan-August) = around 17 days holiday. If you've enough days "in the pot", then you can take the 8 working days. If not... you probably won't be able to take all the time off you wanted.
In addition, your employer may ask you to consider not using the holiday if there is a handover period. There is no reason for you to do this, this would be your decision and would generally only be used to smooth any handover process.
This UK Govt guidance may clear up any questions.