The general rule is that contracts can be made informally; most contracts can be formed orally, and in some cases, no oral or written communication at all is needed.
Thus, an informal exchange of promises can still be as binding and legally valid as a written contract.
There are statutory exceptions to this rule.
For example, most contracts for the sale or disposition of an interest in land must "made in writing": Law of Property (Miscellaneous Provisions) Act 1989.