Short answer: No, not for ordinary mortals. In the 1990's they hosted a wonderful 4th of July party, but 9/11 took care of that in short order.
It is hard enough to get in when you want to discuss something...
As we have very limited counter space and no private area where we
could discuss your case I would discourage you from coming in to the
Embassy. We only ask people to come into the Embassy if there is
mandatory requirement that they be seen in person.
Source: email from the Federal Benefits Unit
The Internal Revenue Service used to operate a walk-in service, which is being curtailed.
If you have a newborn baby who has a claim on US citizenship, you can still get in. It's a large room with some nursery fixtures like a play box. There's about a dozen windows where you get called up according to your number. The ambience is strollers everywhere with screaming babies in various states of distress. Mothers getting angry about the waiting times... The odd diaper change... Normally there's a few people waiting to speak to Social Security or the Veteran's Administration. A bottled water vending machine... A confectionery vending machine... A literature stand with every kind of brochure known to mankind about paying your taxes on time... Not much of touring material.
There's an altogether separate facility for people wanting to join the Navy, etc. People who want to speak to a Navy (etc) Recruiter or enlist will get sent there. Asylum seekers will get swarmed upon by the UK police and hauled away to Yarl's Wood; you can't get in that way.
You'll observe from Grosvenor Square that there's a forward control point outside to screen visitors. You need to be on their list of people with appointments for that day. Americans have one queue, non Americans have their own queue.
Source: US Embassy
If they find a mobile or camera, you'll be sent back to a pharmacy near Oxford Street to check it in, and then when you return you can wait in the queue all over again. You can't even access the forward control point if you have a mobile on your person.
I don't know the procedure for your specific example about US Savings Bonds. My guess is that they would look in your passport and see you arrived just a few days earlier and probably that you acquired the bonds stateside and conclude that it's too dodgy and then turn you over to the British police who would 'ask' you to leave the Grosvenor Square vicinity. But that's strictly a guess.
Opinion divides about what a 'tour' is. So far, this answer has addressed just getting in to the waiting room and consular area. The embassy itself is in an altogether different part of the building which you can't even see from the consular area. It even has its own entrance (which can't be seen from the street).
So if 'tour' means entering the Embassy from Blackburne's Mews and then seeing the reception hall, the gallery, the ball room, the dining room, the state room, the ambassador's office and such. Plus any back office parts like the kitchen, the ceremonial unit barracks, or whatever, then the answer becomes even more trenchant.
My advice: forget it.
This answer is for ordinary mortals only. Of course foreign dignitaries and congressional aides can get in and see what it looks like. Note that local residents in and around Grosvenor Square bitterly and stridently want the US Embassy gone because the security is a blight on the neighbourhood. So perhaps this answer will change when and if the Embassy is re-sited.