Apparently there are still different rules in the UK than according EU OPS. Anyway, according EU OPS any duty before an active flight duty is considered flight duty time in full, however is not considered as an operating sector (OPS 1.1105, 5.2). Therefore it reduces the remaining flight duty time in full, but doesn't reduce it via the number of landings. Deadheading after an active duty is only considered duty and has to be taken into account for the required minimum rest.
So, if one is stuck in traffic on a deadhead before duty its tough luck for the company in any case as the likelyhood is high that the flight has to be either delayed or a standby crew called out, in which case the deadhead might become unnecessary in the first place. After duty one has to inform the rostering department so that the rest time can be adjusted accordingly.
Since deadheading of all kinds is a major thing in my company with more than 50 million euros spend a year on that alone we installed CLAs that regulate how that is done, for example self driving is not allowed at all, the company has to provide transportation in suitable forms from and to homebase.