Thus, would I need to change my flight date?
Since about the time that Internet was invented the Foreign Office has run an advisory explaining that air tickets should not be purchased in advance of an entry clearance application. For this and other reasons, air tickets and related materials like hotel reservations, are not included in the decision-making process.
Or should I be able to enter the country just fine?
Because you are a non-visa national, the Immigration Officer will use Paragraph 23A to land you...
23A. A person who is not a visa national and who is seeking leave to
enter on arrival in the United Kingdom for a period not exceeding 6
months for a purpose for which prior entry clearance is not required
under these Rules may be granted such leave, for a period not
exceeding 6 months.
BUT TAKE CARE: If you are a non-visa national, but hold an entry clearance for another purpose, then the Immigration Officer has the option, but not the obligation to exercise Paragraph 30C of the rules...
30C. An Immigration Officer may cancel an entry clearance which is
capable of having effect as leave to enter if the holder arrives in
the United Kingdom before the day on which the entry clearance becomes
effective or if the holder seeks to enter the United Kingdom for a
purpose other than the purpose specified in the entry clearance.
Needless to say, this can be a catastrophic event and something to prepare for. What they object to is an attempt to get more leave than you were issued (i.e., it is full-on abuse and it gets them upset in a personal way). The ultimate decision is down to the Immigration Officer and the outcome relies heavily on your personal impact and articulation skills.
If you are successfully landed as a visitor, then you will need to channel hop on the day your entry clearance becomes valid. When you re-enter at a port, the IO will put a stamp on your entry clearance and you will avoid becoming an inadvertent overstayer (that's another bad thing that gets them upset).
If, on the other hand, you are successfully landed as a student, the IO will put a stamp directly on your entry clearance and everything's fine and just the way you wanted it. The IO has the option to do this under Paragraph 31, but this generosity is extremely rare...
- Under Section 3(3) of the 1971 Act a limited leave to enter or remain in the United Kingdom may be varied by extending or restricting
its duration, by adding, varying or revoking conditions or by removing
the time limit (where upon any condition attached to the leave ceases
to apply). When leave to enter or remain is varied an entry is to be
made in the applicant’s passport or travel document (and his
registration certificate where appropriate) or the decision may be
made known in writing in some other appropriate way.
I have never seen them use Paragraph 31 to the end-user's benefit and would be interested in hearing about it if you are successful. Finally, if you have any doubts it is fine to ask the IO "have I been landed as a student or a visitor?" Take the opportunity to ask any other questions you have doubts about or do not understand. Doing so will enable you to enjoy your stay here without the distractions of uncertainty.
Compare the cost of changing your current ticket versus the additional cost of a channel hop and an awkward landing interview. The result will usually be changing the ticket such that your arrival date coincides with your entry clearance.