Can I request payment of an invoice within a certain time limit?
Yes you can. From HMRC website https://www.gov.uk/invoicing-and-taking-payment-from-customers.
Your right to be paid
You can set your own payment terms, such as discounts for early payment and payment upfront.
Unless you agree a payment date, the customer must pay you within 30 days of getting your invoice or the goods or service.
You can use a statutory demand to formally request payment of what you’re owed.