London Sites - purchase ahead???

Definitely the Churchill War Rooms. The others I don't know about.

All with the exception of St.Paul’s.

Not certain about April, but in December, I’d say none, since there were no lines. We’ve never pre-purchase an entrance for any London attraction. If you like to have everything planned out, then pre-purchase all of them. We generally like to see what we feel like doing on a specific day, so normally don’t pre-purchase tickets for sights.

I have no personal experience; our first trip to London will be in April--overlapping your dates in part. Our choice was to prebook the Westminster Abbey, the Tower of London, and the Churchill War Rooms, all for first thing AM times. Our rationale is to minimize times spent in ticket lines. Now, with the corona virus situation, I hope that doesn't mean we've wasted the money. Time will tell; we'll see how things look in late March when we are scheduled to depart...

Hope your trip is a good one!

Are you sure you mean Westminster "Cathedral"? The Cathedral is free to enter (and not usually on a tourists agenda):
https://www.london-tourist-guide.com/en/attractions/famous-buildings/westminster-cathedral.html

Willy, we are also going to London in late March and are not even thinking about cancelling-so far UK has fewer cases of coronavirus than does the US.

London has a "reservation" culture, in a way that New York City does not. (Not negating the fact that you have to book Statue of Liberty Crown months in advance, which is really what your question was.) This applies to top restaurants, and to free viewing platforms, like Sky Garden. Even the low-traffic and free London Mithraeum asked me, "Do you have a reservation?". But they were not snooty when I said I didn't, and we got on the next admission time anyway. So when in doubt, buy in advance.

Harelydonski- yes! Both Westminster Abby and Westminster Cathedral. We hear it’s beautiful and has an amazing view of London. Good to know there is not cost. And we LIKE doing things NOT on the normal tourist agenda. We usually mix in a little of both.

Here in the US, I keep hearing that the regular flu strain going around this year is more of an issue than the coronavirus. We have no plans of changing anything.

I agree to definitely check and double check the churches as Holy Week and Easter are very busy with multiple services. Of course, you can always attend a service (although check for Easter Sunday, might need a pass of some sort) but you won’t be able to sightsee.

I’d probably book the Churchill War Rooms, I don’t know if they’ve slowed down since it’s been a couple of years since all the Churchill movies came out, but it quickly exploded to a very popular destination.

Even if you don't buy advance tickets, be sure to check Westminster Abbey's website to be sure it is open to visitors on the day you want to go. On some days it's closed to visitors due to special services.

I’m going to double dip and mention that again. Holy Week and Easter are very busy times and they’re all working churches.

We kind of already figured that would be the case. Prepared to just enjoy what we can access 🤗

To be clear, we have no plans to cancel at this time. Nonetheless, we will watch and see how things progress. IF the coronavirus is still an issue in mid-March, that will mean that is has spread much more widely and we would then likely cancel. Also, to be clear, it won't be because we think we're more likely to contract it in, say, France or England per se. It'll be because of the air travel aspect. And, should bad luck strike, being hospitalized or quarantined abroad carries significant downsides--mainly financial. Canceling also entails a significant financial hit (lost airfares and pre-purchased tickets), so it won't be a decision made lightly.

To put things in perspective, would any of you be canceling a planned trip to China today? We would.

When I went to London in 2018 (two separate trips there that year), I found that many sights, including most of the ones you listed, had a discount for booking online in advance. What I figured out was, except for places that needed a timed ticket like the Churchill War Rooms, the morning of my visit was far enough "in advance" to buy the ticket at a discount.

So, look at the websites of the places you're interested in. If there is a discount for an advance ticket, create an account now from home (much easier on a desktop computer than on your phone!). When in London, if you decide you want to go to the sight, just log in on your phone and buy the ticket that morning. Check if the sight will scan the ticket off your phone, or if you need it printed out before you arrive; if the latter, see if your hotel will do it, or if not, allow some time to get the e-mail confirmation converted to a paper ticket at the sight. At least when I went, some sights did not accept tickets on phones, but this is the kind of thing that changes.

You can visit the Sky Garden as a walk-in guest, at the times shown on their web site, copied below.
**

Sky Garden’s capacity has increased so there are now more spaces for bookings and walk-ins. We reserve free-visitor walk-in spaces between 10.00am- 11.30am and 14.00pm-16.30pm Monday-Friday (exc. weekends) and always try to accommodate all guests where possible although access is subject to availability and not guaranteed.

Alternatively Sky Pod Bar welcomes walk-in guests to the bar every weekday between 7am-10am and from 6:15pm onwards. On weekends Sky Pod Bar operates a walk-in policy between 8am-11am and from 9:15pm onwards.

OP, Westminster Cathedral IS really beautiful, and totally different architecturally to St Paul’s and Westminster Abbey, so won’t feel repetitive. If it interests you, go for it!