Is he offering ANY dates for you to use the accrued holiday before 1 May? If he does, then unfortunately you really should suck it up and accept these dates, and it's a hard lesson for you to learn for the future that if you accrue extra holiday by working more hours in the run up to the Holiday Year End, you need to make sure that you book the relevant holiday in quickly or get a written agreement in advance to roll the holiday into the next year.
He has inherited this situation as a new manager and probably wasnt made aware of the backlog of holiday not yet booked, perhaps not being fully aware of how holiday accrues when staff work additional hours. So I have some sympathy but ALSO this gives him some flexibility to say "this year, as a one-off while I review how this holiday booking system works (or doesnt work), I will approve staff to roll forward holiday into the next holiday year but ONLY with my explicit written approval, and by next year I will have a better system and policy figured out."
If he is unable to offer you any holiday dates before 1 May, then he should allow you to (/get permission from his own boss) to roll holiday forward as an exception. Or, he should pay you at your normal hourly rate for the holiday not taken (few employers like this option!).
His job as a manager is to ensure that holidays are properly rota'd so that everyone gets to take holiday in a fair way according to company policy. Nearly always that still means some compromise, which typically exists on a goodwill basis within the staff team and with the manager, and with some employees trying to game whatever system the company/manager has come up with!
As a new manager he probably feels a bit unsure about creating a precedent about rolling holiday forwards or paying them out, but if it is possible for someone to work say, an extra two days a week in April to cover sickness or holiday, then likely there wouldn't be time to use up the hours of additional holiday accrued for April, and logically those hours might be rolled forward. Equally, letting staff accrue more and more holiday, knowing there isnt time left in the Staff Holiday Calendar to take that holiday, is at best very poor management, and at worst, outright theft from the employee who has earned that holiday.
Typically with Rolled Forward holiday, it must be taken within a short period of time eg within 2 months after 1 May, and there is usually a maximum amount of holiday that can be rolled forward to avoid people creating a massive balance of holiday not yet taken. Also, holiday is only ever rolled forward with management permission and is never automatic. Where I have worked, permission to roll forward holiday has to be applied for and approved 1 month before the Holiday Year End. (Obviously if you can earn additional holiday in that final month, it would be subject to a special approval if there wasnt time to take it before the Year End).
Hope this helps.