I'm from India came to UK on Feb 4th 2014 and I will be in UK till Sept 30th 2014. I'm earning money in Pounds, and paying tax as per UK tax policy. I could save some money which I transferred to savings accounts in India. Now, 1. Do I need declare this transferred amount as other income in while tax return filing 2. or is this amount tax free? or how much is it taxable?
By earning money, I assume you are being paid a salary [and not allowance] in UK.
For the Financial Year 2013-2014: You are still a tax resident in India. India taxes Global income. Hence your salary from 4th Feb to 31st March, needs to be declared as Income. The tax will be at your total tax brackets. India does have a Double Tax Avoidance Treaty [DTAA] with UK, so you can deduct any taxes you paid on this income and pay balance in India.
Please note that it is not relevant whether you transfer money to India or keep in UK, it does not change the taxability.
For the financial Year 2014-2015: Depending on the exact date, you may or may not be a NRI [away for more than 182 days] for tax purposes. If you are an NRI there no tax, else as above para.
Since you have already paid tax to the Government of Uk, no tax will be levied on the money earned outside India. As per the Income tax act, any income received in India in all cases is taxable irrespective of the tax payer's residential status. A NRI after receiving income from outside India cannot be taxed as income because of remittance of such income to India.