I’d say definitely try some different amps with your Tannoy’s if you really do like them it’s worth it. If you want new speakers someone suggested Volti that’s a great though. Their Rivals would be a bit above your budget but not the Razz.
Just saw your post that you're in Sweden have you considered Audio Note? A pair of AN-E's might do it for you and can probably be found used in your price range.