I think the true gray area here is in the meaning of "illegal".
Often it's not that much of a grey area. But it is an area with a few potential minefields for the unwary, backed by some pretty severe punishments. Ignorance of the law is generally a poor defence, and getting your CEO jailed can be career limiting.
It gets a bit more complicated when there's competing jurisidictions and national legislation. So stuff like Cisco is relatively simple. It's a US corporation governed by US laws, so if the US bans exports to Syria, Ciscos can't be shipped to there. They, and most other vendors have export control sections on their websites listing embargoed or sanctioned countrys. So ok, I'm a UK national with a UK corporation and maybe some Americans on the payroll. Maybe I just buy tin from an authorised (or semi-authorised) reseller in say, Cyprus and they ship it to Syria. Or the end-user collects it. UK also has export controls and sanctions, so I could be prosecuted by both the US and UK authorities.
Attempts to work-around this I've experienced have been to try and protect US nationals by keeping them out of the loop. That might work, it might not, either way if TPTB notice, it could be an awkward and expensive legal event. Or sales helpfully suggesting that if the customer finds a Cisco, can't we just manage it? No, because supply of services is also often covered by sanctions. Plus generally it's also a major PITA to properly manage foreign devices, especially with the shift to Cisco-as-a-Service and support, maintenance etc contracts tied to device IDs. Vendors are very keen to use that to prevent grey markets, or unauthorised (ie unmonetised) tin from being bought off ebay. Or even from bankruptcy auctions*.
So the legal route is to apply for export licences, which would mean from both UK and US, and IMHO, the answer is generally 'No'. That can also get expensive, ie lawyers and can be painful. Like finding the product/service code that applies to the tin you're wanting a licence for. Especially if you're like me and get sidetracked by wondering how some of the stuff on those lists might end up being used in nefarious ways. Which can also get FUN! because there might be stuff in export control lists that might need licences even if the country you're wanting to ship/provide services to isn't one of the usual suspects on the naughty list(s).
It can also get FUN!** with other technology like Checkpoint. They're an Israeli corporation, some countries make it illegal to import Israeli products. Then if you're bidding for a client who insists on Checkpoint but has a location in a country that boycotts it, BDS legislation can kick in. It can be illegal to refuse to offer Israeli tech, even if it's illegal in the country it's destined for. Then it's figuring out if no-bidding might trigger anti-BDS sanctions, or what parts of your anatomy you might lose if you won the bid and delivered it. Advice from counsel on that one was to basically submit a generic boilerplate response tweaked to make sure it looked like we kinda tried to submit a winning bid. Not exactly good business, but the cost of defending any legal issues that could arise would quickly exceed any profit from that deal.
* Also makes life a little more challenging for bean counters. You spend $10m on hardware, but it isn't really an asset because it has virtually no residual value. But then the taxman says you can't depreciate it to zero straight away because taxman says 'No'.
** Yes, I've been playing Dwarf Fortress too much. But managing dwarves can be much less stressful than managing a business and sales force. At least when dwarves start making unreasonable demands, they can be met with 'happy accidents', sometimes involving magma. HR would never let me do that kind of thing.