Assuming no other income then yes, actually quite a bit higher. Very roughly half of your 25K salary is untaxed and half is taxed at 20% in a normal year. But if you only work the second half of the tax year then it all falls into the untaxed portion - so you get your 12.5K tax free. Normally you'd pay 20% of 12.5K (2.5k) or roughly 200 per month in tax which you won't have to pay.
So 200 p/m better off or 1.2K per year.
I understand NI is calculated weekly or monthly so no benefit there - but you should check that you qualify for a full year of NI because if you don't it will probably be cheap to top it up to a full year and, assuming you're just starting your working life, then you won't care now but in 40 years time you might regret not spending a few hundred pounds now (in the next six years) How to tell whether you'll qualify for a full year of NI is way beyond my ability but in theory your gov gateway account should tell you once the tax year is over.
I think you have to make sure you're taxed on a cumulative basis, not on a W1 basis otherwise you'll pay too much tax (although you'll be able to reclaim it at the end of the tax year). If your tax code ends W1 or M1 or X then that indicates you're being taxed on a W1 basis.
Also watch out for any benefits like health insurance that might not correctly be captured in your tax code initially. That will work the other way, you'll pay too little tax and have to pay it at the end of the tax year.