The cost of your project will depend on:
How much work is required, and
Your choice of products and fittings.
The fitting work.
A simple switch over of bath, basin and toilet, with no shifting around of items and no additional decoration work to walls or floor will naturally require the least work, and a good plumber will be able to complete this type of job in less than a day so, depending on where you live (as labour charges vary regionally) you might expect to pay around £ 200 for the plumbing. This should cover the cost of new pipe and fittings, providing the original plumbing was in reasonable condition, but you will have to dispose of the old suite yourself and also do and decorating, tiling or floor renovations too.
A more complex job might involve relocating the toilet, moving the basin as well as moving a bath and/or a shower. This will involve several days of work, and if your contractor is also retiling and fitting new flooring the work is unlikely to be completed within a week. A complex project like this must be completed in stages, each in a particular order, to ensure the finished job is to a high standard. (read more here) Several different trades will be involved, and the total installation cost is likely to be in excess of £2000, and in some cases considerably more.
In both of the above cases the price or type of the bathroom fittings will have no influence on the cost. So if you have bought a £500 bathroom suite and want to change the layout of your room, the installation could add a further £2000 to your price. Yet, if your bathroom fittings cost £2000, the installation will still add £2000 to your price.
So very often the actual installation price can be considerably more than the cost of the fittings.
On the product side there is considerable variation in price too. You should be able to pick up a reasonable quality toilet and cistern and have change from £250, but if you want something with a designer name and a little different you could pay £1500 or more. Both will do exactly the same job, but one will have a bit more style and individuality.
Similar price differentials exist for every single product you will need for your finished bathroom, so it is impossible to provide a meaningful “average price”. It’s a bit like asking how much will my new car cost? There is no straight answer, and mostly the approach is to look for something which fits into your affordable price range.
In the bathroom there are considerable differences between cheap products and the entry level offerings of the big brands. If something seems too cheap to be reasonable quality, then it’s probably best avoided!
All things considered, you should be able to completely renovate your bathroom (typical UK size 5 to 6 sqM) with a toilet, basin and bath for around £3000 to include the required work with some tiling to wall and maybe floors. If you add a shower as well then allow another £1000, or if the shower is over you bath £350 might do it. These figures are based on decent quality, but basic products, and are the very least you should estimate for a complete bathroom makeover.
See more about installation and the work required here.