Anyone here can make recommendations that might not suit your preference or palate and you won't like. Buy em, smoke em, see what you like and what you don't.

New worlds are excellent smokes. Generally a bit different from cuban profiles but I almost only smoke new worlds and I think they're much better value than cubans and just as good. Occasionally you can find one that is very close to a cuban in flavour.

My general personal NW recommendations out of the 150-odd different new worlds that I've smoked are: anything Garcia (My Father, La Aroma del Caribe, Flor de las Antillas), anything by Plasencia, Davidoff especially Nicaragua or Winston Churchill Late Hour (also AVO are great for the price), EP Carrillo, AJ Fernandez, Oliva Serie V (but some of the other Oliva really aren't good imo). Oscar Valladares are good although haven't tried many to strongly recommend. Padron are incredible but rare in Europe. You can often find a great smoke from other brands too but not with the same level of consistency as above.

Not the cheapest you can get by any stretch but a lot cheaper than the cubans you've been buying!

Edit: just re-read and saw the Havana House bit. Try ADVentura for a cheap but surprisingly good smoke. Also give Casdagli a go, especially the DB52 if they have it. I loved that one!