Do you have / want reserved seats (or the sort of ticket that is only valid on X departure - some of the advance purchase options are like this) on both the Worthing to London and London to Chester bits?
If so, then the "allow more time" option that national rail offer is probably best bet.
Or book the two parts separately (which may or may not end up with a better deal) and choose how much time you want to have to cross London.
Depending on what time of day you're doing it, the Southern trains from Clapham Junction to Watford Junction can be quite busy - and if you have very specific reservations, there is a chance your ticket may not be valid going this way.
This will involve changing trains at Clapham Junction but there are lifts (attached to the footbridge not the subway.)
I don't know if local rail station ticket offices can offer good deals on advance tickets - someone else may care to offer a suggestion here. If so, it may be easier to go to your nearest staffed station and talk to someone.
If you really don't want to use the Underground, London bus route 73 connects Victoria and Euston - going towards Euston, it goes from stop C in the bus station outside the main entrance of Victoria Station, and will set you down in the bus station at the front of Euston Station.
Going back towards Victoria, you will have to cross the Euston Road and get on at the bus stop near the Friends Meeting House (which incidentally has quite a good cafe which isn't as expensive as those in Euston Station!)
Allow plenty of time for this - on paper, buses are allowed around 45 minutes for Victoria to Euston during weekday daytimes (there are a lot of roadworks schemes in central London at the moment which are not helping, and the 73 goes along Oxford Street which is invariably clogged.)
A rail ticket that includes "via Underground" is not normally valid on London Buses (unless the Underground gets closed for some reason), but if you are a "lady of a certain age" who has an English National Concessionary Travel Scheme pass issued by an English local authority, then this is valid for free travel on London buses (if you're not quite that certain age, bear in mind you can not pay a cash fare on London buses any more and would need either an Oyster card or contactless debit card).
I am not sure whether you need to show non London concessionary passes to the driver or 'beep' them on the machine (at one point, the machines in London did not recognise them because London's Oyster Card was built on different technology.)
