I'll look at this from two different ways.
1) Why do you want wars to be fought with Bows/Swords/Spears as the primary small arms technology?
If it's because the idea of people getting up close and sweaty trying to kill each other seems like something fun to write, well then you're not going to get far with this setting (as in not at all).
The reason being that even if anyone who thought about gunpowder miraculously ended dead for some reason, you'd STILL have a lot of vicious weapons on the battlefield over the centuries that'd make hand to hand combat pointless or a massacre for both sides that no one would want to engage in. Ballistae (with payloads such as an explosive head, the way old rifle grenades worked), Trebuchets, Acids, Repeating Crossbows, normal bows (see the Parthian cavalry and their Parting shot tactics), Bombs, Poison gas (a big issue), Napalm, Flamethrowers would all have been prominent on the menu for warmongers in this reality, and NO faction ever willingly overlooks those techs seeing as how they'd give dominance over the battlefield. Another obvious tech that would be militarized would be cars/bulldozers to RUN THINGS (People) OVER (yeah, no spears are going to stop those).
The other problem with your current premise of gunpowder is how you've made the research taboo. The thing with taboo topics is that they still get discussed. Someone somewhere would perfect the tech, arm his kinsmen and take over the world in the name of Khan (or whoever wins the tech lottery). Because Khan's side would have guns, the rest of the world would go scrambling to get them, either skirting around treaties or just ignoring them in order to get their hands on their own guns (for a fun history lesson on how treaties don't mean much in warfare, see how European nations worked to skirt around the negotiated limits on naval power after World War 1 AND 2, and how Japan today is only allowed a SELF defense force - ergo no force projection aircraft carriers - so it just calls its aircraft carriers amphibious assault vehicles and everyone just nods)
As far as the impact of techs you want would have on the battlefield - Trains were mainly used for logistics, having train technology is more relevant to your world's supply lines and economy than actual fighting (though since they make troop movements fast, enemies would not be able to be sure about how much forces would be committed to regions along the train line). Ships would move away from ramming and swashbuckling to throwing acid or napalm via ballistae. Check out Greek Fire for a technology lost to history. The moment you have things that can fly (zeppelins), you have airbombing via napalm and eventually better conventional bombs, and that'll be a pain for your squishy swordsmen (try throwing flaming spears 8000 feet into the sky, whoever hits the target is the new king of England - a reverse King Arthur scenario if you will.
Of the tech you want, cellphones are in fact EXTREMELY complicated machines requiring hundreds if not thousands of intermediate techs to arrive at (you need a tower network, switchboards, cabling, common standards, computers, and so much more, the whole kit), and I'm sure somewhere down that tech tree the absence of gunpowder would have been a major issue. Also bear in mind that without gunpowder access to exotic resources (such as rare earth metals from China) would be limited, so scientists would have a hard time experimenting with those resources, slowing down tech advancement rates (so your story would have to take place in something like 2500 AD to have cellphones). Smaller empires due to no empire being able to outright dominate others also mean that colonialism, and its child capitalism would not have taken off as much as they have in the modern world, so China, India, Africa, and a lot of other nations would be strong counter-balances to your grand Britannian empire.
2) Now, despite having said all that, you can have a world without gunpowder, but it'll be have to be like the world mentioned above - close range combat will still be obsolete and a total no-go. If you can work with that in your scenario then by all means go ahead and surprise us.
~StrykerL out