More or less.
The important this is whether your employer has you on PAYE (pay as you earn) or not. In most cases you will be and work will automatically deduct tax/national insurance from your gross salary, paying it to HMRC for you.
If so, your payslips will show the deductions and show your gross (before tax) and net (after tax) salaries. If not, you’ll need to register with HMRC online to self assess.
As Keith says, they work it out based on your salary so you should pay an even amount of tax each month rather than nothing for a few months and then loads at the end of the year.
There are a few scenarios where you need to register for self assessment regardless, but unless you’re making a lot of money outside work or paid within the top 5% or so of the country they don’t apply to you.