Contact
Talk to someone who has run a chain
If you are ready for a quote the form is quicker. If you have a question first — about completion day, about the hold, about a date that might move — this is the place.
The most useful first email says both addresses, the number of bedrooms, and where you are in the chain. Even "we have had an offer accepted and no date yet" is enough to start.
If your date is already in play
Say so in the first line. A move with a date already agreed in a chain gets looked at before anything else, because the borough parking applications have their own notice requirements and those are the constraint.