HP ink cartridges
I've used www.inkclub.com for years and have always been happy. They have original and 'own brand' cartridges. I've no idea whether the prices are particularly competitive as I'm happy with the good service.
Delivery is by post and you pay by bank transfer after receipt
I also use https://www.inkclub.com/be/fr/. Very good service, prompt and reliable. You enter your printer model, and they return the various options.
For example, the Deskjet 1180c uses the two cartridges you quote, 45 & 78.
They offer the original HP cartridges, or off brand cartridges at a substantial discount.
I suggest a Google search 'cheapest ink cartridges for HP45 and 78'.
I got all my double easy pack ink cartridges from a UK website; ordered and for it at the weekend. Despite the exchange rate and postal costs it was globally a lot cheaper and arrived 4 days later.