It can get messy, if you have the same (standard) tax code for each job then you will be paying TOO LITTLE tax, this will be calculated on your self-assessment after the end of the tax year and you will be given options how to pay it back.
If both jobs are (roughly) stable income and long term then you can get two separate tax codes for each job which will be calculated to charge you approximately the right amount of tax, again, at the end of the year your self-assessment will work out any correction. iirc one employment has to be decided to be the "main" job even if both are equal. If the second employment is substantially less income it can be trickier.
It is not uncommon for one of the pair of tax codes to be zero or near to zero.
The reason you would be paying too little tax is that you would get two allowances (currently £7,475 for single person) before paying tax, so if (say) both jobs were equal income then you would be earning £14950 before paying any tax instead of paying tax only above £7475.
Despite all the horror stories, the tax offices are quite friendly and a phone call will sort things out (plus the forms).
As a slight aside, if you've never done a self-assessment, these aren't too bad when you do them online, the first time is scarey and difficult because you end up chasing banks etc for figures, but once you know what you need, the next year is easy. I was going to list them but my memory isn't that good, but basically you need to know amounts for anything you earn, anything you gain interest or profit from, any inheritance, any capital gains (selling house, shares) and any gift aid donations you've made.
In a time of universal deceit - telling the truth is a revolutionary act. George Orwell
When the debate is lost, slander becomes the tool of the loser. Socrates