It's not unusual for tax amounts to vary in the first few months of employment, particularly if there's a period where your P45 hasn't yet come through. If you're unsure, you can ring HMRC and get them to take a look. I would guess that in your current job:
Month 1 - no P45, so no info about what you'd earned since April 2018 or tax you'd paid. Your pay would have been calculated based on zero previous earnings, so you would have been charged very little tax.
Month straight after you submit P45 - previous earnings and tax now known, so system will adjust not only what tax would be due that month, but also any underpaid tax from previous month(s)
Following month - pay and tax should stabilise and be the same from this point on (assuming no changes in tax code)