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Tl;dr
If a) the vaccination reflected in your certificate is one of the vaccines specifically listed on the Luxembourg government webpage you cite, and b) the vaccination pattern meets the requirements of the same Luxembourg government webpage, then you satisfy the Luxembourg covid requirements and may enter Luxembourg under the current Covid regulations.
A More Complete Response
Insufficient information is given in your question to determine the answer.
The Luxemburg government page you cite prohibits entry into the country, with several exceptions. The page says this:
Restrictions apply with regard to persons authorised to enter Luxembourg.
Citizens of the European Union Citizens of the European Union and of the countries associated with the Schengen area, as well as citizens of San Marino, Andorra, Monaco and the Vatican/Saint See, are free to enter the territory of the Grand Duchy of Luxembourg...
You do not qualify under this exception.
...Or if they meet one of the following conditions:
if they are in possession of a certificate proving a complete vaccination pattern that is considered equivalent in Luxembourg. The validity of the vaccination certificate is set at 9 months from the date when the vaccination pattern is considered completed. The validity of the certificate for the booster vaccination is unlimited (see FAQs);...
You might qualify under this exception.
The page cited above defines "complete vaccination pattern" as follows:
Which vaccination certificates are acccepted in Luxembourg?
In order to have a vaccination certificate recognised in Luxembourg, 3 cumulative conditions must be fulfilled:
• the vaccine administered must be accepted in the Grand Duchy (see list below)
• and the vaccination pattern must be considered complete (see definition below)
• and the certificate must be issued by a Member State of the European Union or the Schengen Area (EU27 + Iceland, Liechtenstein, Norway, Switzerland), or by one of the following third countries: (list omitted here)
Addressing each bullet point:
The vaccine must be one of these types:
- BioNTech Pfizer / Comirnaty
- Moderna / Spikevax
- AstraZeneca / Vaxzevria
- Janssen / Vaccine Janssen
- Covishield (Serum Institute of India Pvt. Ltd (SII))
- R-Covi (R-Pharm)
- Covid-19 vaccine (recombinant) (FIOCRUZ)
The second bullet point (vaccination pattern) requires:
A complete vaccination pattern means any pattern that defines the number and interval of injections necessary to achieve sufficient protective immunity and is complete upon administration of the required doses if multiple doses are given or, for single-dose vaccines, after a 14-day interval. For persons who have recovered and have been vaccinated within 180 days of the first positive NAAT test result, the vaccination pattern is complete 14 days after the administration of the single dose of any vaccine administered.
Finally, the third bullet point lists the countries whose national certificates will be accepted. You assert in the question that your vaccination certificate was issued by the United Kingdom, whose name appears on the list of countries.
Thus, if a) the vaccination reflected in your certificate is one of the vaccines specifically listed in the first bullet point, and b) the vaccination pattern meets the requirements of the second bullet point, then you satisfy the Luxembourg covid requirements and may enter Luxembourg under the current Covid regulations.