So to beat England, you would need a lot of cavalry. England is the best archer faction by far, especially when they're spamming lomgbowmen. If you're talking of English units specifically, Byzantine missile cavalry can beat almost every English unit except for the archers. Because of this, you should be able to pick them apart with the missile cavalry quite easily. Then there is Venice and Sicily, as Italian factions they have extremely good infantry and heavy armor, but are completely lacking in cavalry (except for the Norman Knights). That is your key to pushing north and east.
I would use them along with Byzantine Spearmen against other cavalry-dependent factions, such as Hungary and the Turks. Byzantium has the best missile cavalry in the game, so they are to be used a lot. Hello KostasHBK, and welcome to the forums! I have a lot of experience from playing as the Byzantine Empire, which is probably my favorite faction as well