No, it’s very unlikely that there are any strong programs in your field (not just Ivy Leagues - that’s just an athletic conference. The Ivies may not even have a PhD program in your area at all) at this point in the year. If you have no funding, I would just wait to apply for Fall 2022.
One thing to consider: aren’t UK PhD programs shorter? Funding in the US barely covers living expenses, if at all, and it can be 6-7 years. If you compare finances for the two scenarios, shorter program with funding versus longer program with funding, which works better for you? The UK option also means more post-PhD years working.
Dollars to donuts it’s still a funded program.
In the U.S., most funded PhD programs cover tuition, fees, health insurance, and a stipend that usually ranges between $20K and $35K a year. Although that’s not a lot, it is enough to cover a very modest standard of living in most places. Top programs in most fields (which is what I assume the OP means by “Ivy League”) are going to pay a stipend that is going to be enough to cover living expenses - so I would actually say it is safe for the OP to assume that funding is enough for living expenses. In fact, I would go so far as to say I would turn down any PhD funding offer that isn’t enough to cover living expenses.
An unfunded student in the U.S. is going to at least have to take out loans to cover tuition, fees, and health insurance. In the EU, that may not be as much of an issue, but you will have to find some other way to cover your living expenses. You’re going to come out ahead in a funded program in the U.S. almost every time - it kind of doesn’t matter how long the program in the UK is (although they are usually about 3-4 years. PhD programs in the U.S. are about 5-7 on average).