Your existing bike should be fine (not ideal, but that is a different matter). Just take as little as you can, and load it in a Carradice saddle bag with a support. Make sure your seatpost and saddle rails can handle the load. To prepare your bike a bit I would fit the widest posible tyres (Panaracer Pasela 25 mm, or perhaps even 28 mm if they fit). Use SKS Raceblade mudguards to preserve as much clearance for wide tyres. Get lighter gearing: fit the largest cassette your RD will handle.
If you like it, the real fun, however, will be in loaded touring with camping gear. For that, your existing bike wil not do. Get a Surly Long Haul Trucker or similar. By staying out of hotels restaurants etc you will save enough on one month summer holiday to pay for the bike (1000 pounds), and for a quality lightweight tent (400 pounds, mattress (100) and sleeping bag (200). All depending on the cost of hotels etc, but I don't think I am far off. And it is so much more fun.