Well if you plan to immigrate , go for US. Because the visa system is much more complicated in UK .Also you'd need hell load of pounds to start a fresh living in UK. Start with 2500$ a month in US. I've added an extra margin to your budget since you need to look for affordable accommodation and a decent salary job.
Now I'am definitly confused , I know it's tow different countries but price can't be that different .
WhatTheGox said I need around 5000$ to stay for six months as a start (time to finda job etc ... ) and you are saying that I need 2500$ monthly or I can't live there

as I said I know he was speaking about UK and you are speaking about US but it can't be that different
Yeah $5k or £3000 GBP would be a safe amount to move to UK imo, it really depends. If i were you i'd try and make some friends if you cant get savings going without a job in wherever and maybe you can go for cheap, stay on the sofa maybe. I have no idea on current immigration laws remember, or your ability to steal friends sofas for long periods