I have moved to UK on 10th Feb 2018. And Tax amount around £1300 has been deducted for months Feb and March because I didn’t have NI number for first 2 months and also it was end of financial year. my monthly salary is 3500. can anyone please help me how much money I can claim back?
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You are probably going to get most of this tax back.
When you move to the UK you are considered resident for tax purposes only for the part of the year when you are actually in the UK.. This means that for UK purposes your total income for the tax year is going to be your income between 10 Feb and the end of the tax year - so not much. you will not be assessed tax on any income you earned abroad before you moved to the UK. Unless you are a high earner, this will most be offset by your personal tax allowances, and you will end up paying minimal tax.
Of course you will only find out exactly how much when the tax office finishes collecting your data and sorting out your situation. It's possible to predict it roughly, but certainly not without knowing your exact salary and other income. When they do finish they will return some of your tax paid, either through your employer or by sending you a refund cheque. You could help the process along by filing a tax return, but it probably isn't necessary.
Some points to be aware of:
If for some reason you had other UK income from before you arrived in the UK (investments for example) that will increase the amount of tax paid.
Your previous country may require you to pay tax on your UK income.
Only tax will be refunded, not National Insurance contributions.
HMRC (the British tax office) keeps track of your income and tax contributions automatically, and most people don't need to do anything to ensure they pay the correct tax. However this does rely on you having an NI number, and your employer knowing and reporting it. When that has happened you should find that your excess tax is returned to you without having to do anything, probably through your paycheque. You may possibly need to fill in a self-assessment tax return if you have British income other than your pay, or other unusual circumstances. Check the link above to see if it is necessary. British tax returns are pretty simple and you should not need any help doing it, certainly not a 'third party vendor'.