Your printer should accept third-party inks as long as the firm producing the cartridges has reset the chips in them.
The company I normally buy my inks from, Inkredible, is currently out of stock of all HP 301 inks. My back-up supplier is a bit cheaper than some other places though:
https://www.premier-ink.co.uk/printer-cartridges/hp-printers/hp-envy-range/hp-envy-5530.html
Realistically though, it might work out far cheaper in the long run to buy another printer (which wouldn't necessarily cost more than the equivalent of a couple of HP 301 cartridges anyway) and to do your research first to find one which uses cheap inks. For example, I pay just £14.41 for a full set of all FIVE cartridges for my Canon printer (with that price dropping as low as £12.89 if I buy in bulk).