Changing trains London Euston to tube-to London Waterloo: Enough time?

Totally feasible. The tube journey (on the Northern line southbound) itself is only 6 stops- 8 minutes. Platform to platform it's an easy 30 minutes- I've done it in 15 minutes when pushed.
If the Avanti train is late and you are on a through ticket as you seem to be, then you are automatically entitled to take the next train from Waterloo, without having to do anything. The trains to Brockenhurst are every half hour from Waterloo.
All the signs at Euston are very clear, but just check you get a via Charing Cross train, not a via Bank train.

That’s loads of time.

When there are multiple changes on a journey like this it’s worth pricing the legs out separately.

For example two adults with a Two Together railcard

Conwy to Crewe £39.60 Anytime ticket

Crewe to London £31.60 Advance ticket

London to Brockenhurst £13.50 Advance ticket (plus Tube fare across London)

Play around with https://www.nationalrail.co.uk/ and you might get the prices down further.

Just make sure you avoid rush hour in London.

In case it is important to your circumstances, you cannot avoid stairs completely using the Northern Line route.

I would pay extra and have only two changes. If I had to make that connection in less than an hour, I would be a nervous wreck. Even if you're traveling light, you will have to drag your luggage in and out of a train two fewer times.

With that said - you have received helpful suggestions, and you know your own comfort level.

The split fares quoted above are not correct fares for the OP's day of travel. I have had the OP's original post bookmarked and on follow up for several weeks, because I follow up cases to their conclusion.

The fare the OP is quoting are 'open singles' allowing her to travel on any train that day on the line of route, not restricting her to that particular train which is booked- which is the most expensive option available (other than the via Birmingham route).

What worries me more is that the OP is travelling the North Wales coast line on a Bank Holiday Saturday, with the first two legs Conwy to Chester and Chester to Crewe being on TfW's 2 car trains, on which no seats can be reserved, at a time of day when they could be very easy.

I, personally, would have opted to travel ex Llandudno Junction (with or without the local train across the bridge from Conwy to LJ) on the earlier through Avanti 5 car service from LJ to Euston, which almost certainly attaches to a second 5 car unit at Chester to form a 10 car train forward.
That train is much more likely to give a comfortable journey.
Some people also like the comfort of a through ticket rather than fretting about connections between separate tickets -however, for completeness, the correct split in the example quoted above is £15.90 + £50.10 + £17.50, for that particular day and combination of journeys.

On the earlier through train the same split would be £39.60 + £44.80 + £17.50, but of course you could end up having to change seats at Crewe (even having to switch between the 2x 5 car units- which has to be done on the platform as you can't walk inside the train between the units), booking it that way- as the system may allot you different seats for the 2 parts of the through journey.
My view is that the OP has had a lot of advice on this journey- if she wishes to book unrestricted through tickets that is her prerogative.
And yes I do know about the unreserved coach on the train, but joining the train well into its journey that might be full at LJ- unlikely but possible.
There are plus and minus points to either approach.

Many thanks to all of you for your prompt and useful tips. Unless the price has jumped up higher than today’s price, we will probably take the Conwy-Southhampton-Brockenhurst route, with only two changes.

Sallytravels will be pleased to know that the price of the two change route can't go up as those are open singles. It can only go down if advance fares happen to appear.

I am pleased to see that the ticketed route on that ticket is a change at Wolverhampton- which is easy, so you avoid the dreaded change at Birmingham New Street.
Southampton should be a same platform change. So a lot of positives to the more expensive route.

Just for the record, if you wanted to shave £50 off the fare, Conwy to Wolverhampton is available as an advance fare for £29.10 for two people 2T.
For a robust connection at Wolverhampton you could have lunch in Wolverhampton (the station is very central) then get Wolv-Southampton an hour later at 1439 for £146.30 Open Singles.

One BIG WARNING- the Wolverhampton to Southampton train will NOT run as booked as it's route is via Oxford. The bridge work south of Oxford will not be complete by your date of travel, so you will end up on a rail replacement bus between Oxford and Didcot, which will add 1 hour to your journey time.

I'm not sure that I agree with everything just above.

Wolverhampton station is pretty much a desert - having worked trains in and out of there for decades I speak from personal experience, and to find much to eat will involve leaving the station and going for a walk.

Birmingham New Street was, on the other hand, was given a major face lift several years ago and is much better than it was a few years ago. It, in contrast to Wolves, really is in the middle of everything, and has many different food outlets both within the station and in the Grand Central centre which surrounds and is on top of the station. All platforms are served by lifts, stairs and escalators, at different places along the platforms. There are plenty of staff for question asking, and a help point just under the big screen.

I might be asked - have I ever changed trains at either Wolves or New Street - the answer, yes, many times at both. And when the rain, sleet or snow is coming down I much prefer New Street which is nearly completely under cover (except for platform 4C which has the trains to Stafford, Crewe and Liverpool) as opposed to Wolves which is nearly completely open to the weather.

Nigel, I just noticed that there are no stations in or near Conwy where I can collect my train tickets from Conwy to Wolverhampton to Brockenhurst. We have not yet purchased them (2 Together), but I’m just wondering what we should do if and when Advance fares become available. Can the tickets be issued online?

At this moment I see a fare of £104.40 for two people (2 Together) leaving Conwy at 9:14 on 27 June with change in Filton Abbey Wood continuing to Southhampton Central and arriving at Brockenhurst at 16:39. Is £104.40 a good fare, or shall I wait until next week to purchase?

Thanks so much for all of your help!

Conwy is an unmanned station. It's basically a platform and some benches. No ticket office, no ticket machine. Buy your tickets online.

If you are seeing a fare of £104 for two jump on it- that is a great fare. In fact I think it's brilliant. It will only go up.

Filton Abbey Wood is an unusual place to change but that is by the by. I don't remember there being much to the station but that's irrelevant- it's just a change point.

I had been thinking about a variant of that route- which would be Conwy to Newport, Newport to Southampton and Southampton to Brockenhurst- two easy changes (and the same train as you catch at Filton AW) which to me is a good non London route, but I struggle to make the system offer as a through ticket.

As you are doing several rail trips earlier in your vacation, any rail ticket purchased on line can be collected from any ticket machine in the Country (not just your station of origin) at any time from 15 minutes after purchase until the moment of departure. So earlier you are in Norwich and Canterbury, among other places. You can pick up your ex Conwy ticket at any of those places,
or buy it as an 'M' [M for mobile] ticket which you show on your 'phone.