Changed my mind :)
Baby first aid kit - calpol, thermometer, bonjela, ibuprofen, plasters, nasal spray, cough syrup
Changing bag and contents - nappies (prob size 4 or 5, Aldis are great), wipes, nappy bags, bum cream. Baby sun lotion. You get a nice free changing bag if you join boots baby club and it's still going strong for us.
Baby plates, bowls, cutlery, cups. IKEA do nice ones and tommee tippee cups are nice.
High chair (ikea again)
Bottles, maybe one tin of formula if he hasn't been weaned off it yet. Other wise blue cows milk. Milton sterilising tablets if he is still on formula.
Changing mat
Cot, mattress (needs to be new) fitted sheets, mattress protector, light blanket or sleeping bag in this weather
Group 1 car seat. We have gone for the maxi cost axis as can't afford rear facing
Buggy - we have two, a big travel system (Quinny buzz) and a more compact umbrella stroller for holidays (Chicco something). Start a new thread for buggy advice :)
We don't use anything in the bath other than toys and shampoo, he uses our towels etc
A few toys - don't go mad! DS's favourite is a wooden Noah's ark, and tomy hide and squeak eggs. Other than that, lots of cups/bowls, our phones/remotes/keys 
Clothes - agree to wait and see what you get, but about 7 vests, 5 sleepsuits, a couple of pairs of pants and a few tops should see you right. Socks and a sunhat too. Bibs are always handy at this age.
Find out what food he likes but I would have thought he is feeding himself a bit at this age, google blw for food ideas.
I hope that helps! A month is plenty of time. I will keep posting if I remember stuff.