The number of nose jobs, face lifts and breast implant operations all soared by more than 10% last year.
The biggest boom was in the popularity of liposuction - up by 41%.
Baaps said it was "the most impressive rise in demand" since the start of the recession in 2008.
There were 50,122 cosmetic procedures in 2013 - a rise of 17% on the previous year. Baaps said the increase had been "across the board".
The top 10 procedures were:
Breast enhancements were the most popular operation in women, while nose jobs were the cosmetic surgery of choice in men.
Rajiv Grover, a consultant plastic surgeon and president of Baaps, said: "Both the UK economy and the British public seem to be well on the way to regaining their shape with the most impressive rise in demand for cosmetic surgery we have seen since the onset of the recession in 2008.
"The continued double-digit rise of cosmetic surgery underlines the fact that whether it is breast augmentation or anti-ageing procedures like face-lifting, the public are choosing tried-and-tested surgical methods rather than the magical-sounding quick fixes that fail to deliver promised results."
The reputation of the cosmetic surgery industry was brought into question during a scandal involving faulty breast implants.
A lack of record-keeping meant some surgeries were unable to tell their patients if they were affected by the recent scare over sub-standard PIP implants.
Health ministers described it as a "cowboy industry" steeped in "murky practices".
In January a new register was set up to record the details of every breast implant operation in England.
Fresh efforts are also being made to regulate adverts for surgery, to end the era of "win a boob job" competitions.
The industry was worth Â£750m in the UK in 2005, Â£2.3bn in 2010 and is forecast to reach Â£3.6bn by 2015.
There has been a dramatic increase in the popularity of plastic surgery in the UK, according to figures from the British Association of Aesthetic Plastic Surgeons (Baaps).