There will always be demand (although the peaks and troughs of our economy will not always guarantee work), your limits will be set by your drive and determination as much as an ability to work with plans, making accurate measurements, attention to detail, dexterity and craftsmanship.
With experience, starting your own business is probably the way to make the most money but is also the highest level of commitment and not without risk. You will need a good sense of business savvy but the benefit is you are your own boss and nothing comes close to that feeling for job satisfaction.
As for income, carpentry covers a range of skills so it all depends on your aspirations and where you see your level of ability.
At the lower end, 'chippies' more formally known as joiners, work on building sites both commercial and domestic. They will provide services ranging from stud partitioning in walls, to roofing and flooring, staircases, windows, patio decking, sheds, doors, lock fitting etc. The available work depending on the scale of the development will either be contracted out to a local supplier (larger projects) or smaller outfits including self-employed joiners.
In the middle would be joiners fitting bespoke items like interior fittings for bars, restaurants, offices, kitchens and storage wardrobes, bookcases, theater, film and TV sets and many other projects.
At the highly skilled end would be furniture makers, high quality items either bespoke hand made or factory produced finishers.
The skills required will be wide ranging from a basic apprenticeship gained as a joiners 'mate' on construction sites, to many years of learning skills as a designer and craftsman.
Career progression with suitable college qualifications and within an established company could be supervising, project managing, estimating, buying, training and the like.
Expect £15k to £18k whilst training, £22k to £30k as a skilled employee with several years of experience and £40k+ as you progress into management positions.
Having established your own company, your profit will be down to how much business acumen you have and your own drive, determination and motivation - from none at all to the skies the limit.