I am a student in the UK. I am currently in a red list country and the Hotel Quarantine is too expensive. If I travel to a country that is not on the red list for 2 weeks and then travel to the UK, will it be a problem?
In theory, yes. But beware of the many caveats:
First of all, of course, you need a country that would let you in in normal (non-Covid) circumstances, most likely without a visa. Depending on your nationality and personal circumstances, this may be easy or quite difficult. Remember that you will most likely be outside of any transit-without-visa (TWOV) regimes.
You need to make sure they they would accept people coming from the country you are currently in, including people who are neither nationals nor residents (some countries only allow nationals or residents to enter from some or all other countries).
You need to make sure they will accept you for the given reason (some countries will only accept visitors for specific reasons).
They will most likely require one or more PCR tests before and/or after your arrival.
They may impose quarantine, either in a managed quarantine facility or at home (possibly with quite a few restrictions on what "at home" can be).
You need to remember that they may change their own criteria of admission (countries they accept people coming from, limitation to nationals/residents, reasons for admission), sometimes at a moment's notice. A country on the UK's red list has a strong probability of appearing on other countries's red lists.
You need that country to not be on the UK's red list.
You will need to quarantine upon arrival in the UK (though not in a hotel, so it could be cheaper, but remember that home quarantine rules are quite restrictive nonetheless, and imply a certain level of organisation — and cost — just to be able to eat something).
You will need to book and pay for tests before your arrival in the UK and during your quarantine.
The country may be added to the UK's red list at any time. At the moment there are probably more countries risking being added to the list than removed. You mentioned Turkey which has a strong probability of being added to the list shortly, given the current trend (though criteria for inclusion are unclear).
Flights may be cancelled or rescheduled based on evolving restrictions.
Given the duration of the stay in the third country, the flights will most likely be priced (or even booked) independently, so the cost may be higher (though that is highly variable).
You'll have to factor in the cost of transportation to/from the airport in the third country.
All in all, yes, it is probably still going to be cheaper, but not necessarily as much as you think, and there is a high risk that you would either be denied entry into that third country, or that you need to undergo hotel quarantine in the UK anyway, depending on updates to the travel restrictions of each country.