In general this policy is set per-University and sometimes per degree program, so its impossible to give a one-size-fits-all yes/no answer to your question. However, in general every program should explicitly specify on their website about materials required (such as a TOEFL score), including information about who (and how) you can be either exempt from providing a TOEFL score or whether or not your current score can be accepted.
However, if you are specifically referring to the TOEFL iBT, the ETS states that they are only valid for 2 years:
TOEFL scores are valid for 2 years after the test date and there is no
limit to the number of times you can take the test, but you cannot
take it more than once in a 12-day period.
As for officially stated policies of a University, as an example from the University of Michigan's College of Engineering international graduate student's requirements (2018):
Exceptions to the English proficiency tests include only lifetime
residents of Australia, Canada (other than Quebec), New Zealand,
United Kingdom or the United States (other than Puerto Rico). Students
who have recently and successfully completed at least 4 years of
rigorous academic studies in one of the countries listed might also be
exempted if SAT critical reading scores are in the mid-600 range.
Applicants that meet the above criteria and wish to request an
exemption from the English proficiency requirement must present SAT
scores and send a written request containing full name...
Test scores are valid for two years from the date an application is
received. Expired scores will not be accepted.
So for this specific program, you would need a more up-to-date TOEFL score according to official published policy, as your scores are more than 2 years old. You would also not meet the requirement of "at least 4 years of rigorous study" in the UK, so you would also be less likely to be given a waiver from this requirement.
You will basically need to check these requirements for every program you wish to apply to, as some programs have more or less stringent requirements.
Ultimately I could foresee you having 3 options:
1) Don't apply to programs that won't accept your existing score.
2) Email the the program, specifying your specific situation, and ask if your existing information would be acceptable.
3) Take the TOEFL again. It certainly won't be the only part of the process that doesn't seem like it makes any sense! Most programs require the GRE, too - even though it has a reading/writing component in English, most programs will probably still require a fresh TOEFL score.
A fourth option of "apply anyway and see what happens" is less advisable, as you'll probably be spending 75$+ per application only to have your materials thrown out and no money returned if they decide not to accept your out of date materials. I wouldn't suggest it.