In addition to list above:
Stanley knife
Spirit levels
Pliers
Pencil
Felt pen
Blow torch
Spare gas
Solder
Flux
Heat mat
Scissors
Plasters
Insulating tape
Multimeter
Push fit stop ends
La-co slictite
Loctite 55
PTFE
Funnel
Pump and pressure gauge
Weir gauge
Long schraeder valve
Pressure tester
Drill bits 1.5mm to 10mm
Various larger drill bits
Tile bit
Tile cutter
Trowel
Tile trowel
Mixer
Buckets
Towels
Abrasive pads/wire wool
Spare pencil for lending to customer
Spare pencil for lending to builder
Spare pencil for lending to electrician
Spare pencil for lending to joiner
WD40
Torch
Toolboxes
Organiser boxes
You can easily spend £000's if you don't watch yourself. I've just bought 7 screwdrivers, 4 pliers, small Knipex pump pliers and a thin bladed Bahco spanner with a few other bits (biros, scissors, latex gloves) and spent something like £200.
For £200 you could buy a whole cheap, hand toolkit then replace the worst tools for better quality ones as and when you start making profits. This will give you a decent tool as well as an old tool that you don't mind getting mucky. For example, I use an old pipe cutter when cutting existing pipes and a new one for clean copper tube.
I spent around £300 when I got going and added to my tools as and when I required them and probably have around £1,500 worth now. You don't NEED a wet vac but it does make some jobs much easier. Ice cream containers and towels are just as good, if a little slower. You don't NEED Bahco spanners and Knipex pump pliers on your first few jobs but when you use them instead of cheapies, you'll be glad you did. Only when you start working will you know what tools you really want and really need. Before you get going it is quite a guessing game. You'll also meet other people and wish you had spent your money on something else instead.
Cashflow is so important when you get going and the more cash you put into assets (tools) the less you have for all your other business expenses. You can make good profits but can still go bankrupt with a poor cashflow policy.