House deeds often have limitations, mothers house can't keep chickens for example, and businesses run from house are very limited, often Doctor, Dentist, and Solicitor is allowed, but not much else.
But be it keeping caravans in the garden or any other thing officially not allowed, in the main it needs some one to complain first. So there are things you can do to minimise disruption to other people, using inverter welding machines, and inverter drives can reduce the start up loads and with it the dimming of lights etc. Not only will they reduce the start loads they will also reduce cable size required. So step one is to find out what you want to run with start up loads in mind. No one can simply say you need a 16mm² cable to weld with, they have to know what welder you are using.
I found a standard welder runs on 25 volt plus 1 volt per 25 amp so a 100 amp welder will be around 29 volt and a 200 amp welder around 33 volt. You need the volts to work out current, so 100 x 29 = 2900 VA divide by 230 volt = 12.6A so about the maximum from a 13A outlet, at 200 amp = 28.7A at 230 volt. This is approximate but it gives you something to work with. So welding using TIG or MIG is not that much of a problem, normally below 100 amp and normally an inverter as want a DC supply. Stick welding is another kettle of fish.
As to lathe well using an inverter also gives speed control to some extent so one designed to work with an inverter can have less mechanical speed control, this is all well and good when looking at a new lathe, but looking at an old Milford 7 some mods would be required to convert to inverter control, here it depends on your skill, to be frank every inverter seems to have different instructions so even an electrician has to follow the instruction book, but few inverters are less than £100 many are around the £500 plus you would want a 3 phase 230 volt motor, smaller motors tend to be 230 volt delta and 400 volt star so a three phase lathe may be able to run on 230 volt three phase from an inverter. Normally you need an inverter per motor not one inverter to run the lot.
Until you have weighed up pros and cons of inverters you will not know how much power you need. Likely you will only use one machine at a time, so only really interested in the biggest power user, again since you will likely get volt drop and you have rotating machinery you need to consider lighting, many LED and fluorescent lights can cause a stroboscopic effect. So likely you will want HF fluorescent or DC LED lighting. The HF fluorescent normally has a large voltage range some can be 85 ~ 250 volt although most will not drop that low, so again this all relates to cable size, and volt drop.
Distance will also effect volt drop.
Although a piece of string which runs in the centre of a cable is 185.2 meters long, not all bits of string are that long, so we talk about the length of a piece of string as being in the main an unknown quantity, it's the same with your question, although we could guess that 6mm² SWA cable will likely do the job, in real terms we don't know. And it is likely a balance between what you pay for your equipment and what you pay for the installation.
Location is also important, if your house is close to a large transformer then your equipment may not cause any noticeable volt drop. However if supplied from a pole mounted transformer it could be a massive problem. The loop impedance or prospective short circuit current would give one a clue, but this is really a job for some one on site, not people on a forum.
