Is it permissible to take an interest-bearing loan from the British government for the children's education with the intention of not repaying it after graduation and travel, and is this considered permissible?

It is not permissible to take a loan with the intention of not repaying it. Rather, one must intend to repay it at the time of borrowing. If the intention to travel after graduation is aimed at not repaying the loan, then this intention is impermissible. However, merely intending to travel carries no sin. As for the ruling on the loan itself, it is unlawful if it involves usurious increase. Some contemporary scholars make an exception for those who have no other means to complete their education except through a loan.