Can spanish troops help the french attack on London in the french turn and vice versa?
No, because the two powers haven't taken combined movement. Either declaring a siege would force Great Britain to roll for besieged supply, but if both wanted to attempt an assault, each would do so individually.
This would mean, that they got two chances to break into London the same turn?
This is correct.
In my opinion they wouldn't be allowed to help the attack in their allied turn, as long they aren't combining their movement, but I'm allied to Great Britain.
You would be incorrect - the rules very clearly require that a power that wants to participate in an siege does so in its land movement phase, which is different when powers have not combined. This does mean that Spain and France get two attempts to force a breach, but it also means that each attacks with their individual numbers and morale, which has the potential to cause both attempts to fail even if a breach is achieved (lower casualties when the French attempt, lower morale when the Spanish do).
Look at it this way - would you permit powers that were not combined to act together in ways not permitted by the rules in other portions of the land movement phase? Could a Spanish corps somehow move during the French movement phase? If the answer to that is "no," then why would this be different? The rules call out specific times when uncombined allies can take action (reinforcing a land combat, for example).