Here are the requirements and conditions for top UK universities, based on common standards for PGR programmes (like PhD/DPhil):

1. University of Cambridge

1. Requirement: Typically requires the Higher level.
2. IELTS Academic: Overall score of 7.5, with a minimum of 7.0 in each element (Listening, Reading, Writing, Speaking).
3. TOEFL iBT: Overall score of 110, with a minimum of 25 in each element.
4. Conditions:
5. Results must be from a single sitting of the test.
6. The test must be no more than two years old at the start of your course.
7. Some exceptions apply if you have recently completed a degree taught and assessed in English in a majority English-speaking country, but this is assessed on a case-by-case basis.

2. University of Oxford

1. Requirement: Requires either the Standard or Higher level, which varies by course. Many arts and humanities courses require the Higher level.
2. Standard Level IELTS Academic: Overall score of 7.0, with a minimum of 6.5 in each component.
3. Higher Level IELTS Academic: Overall score of 7.5, with a minimum of 7.0 in each component.
4. Conditions:
5. Scores must be achieved in a single test sitting.
6. Tests must be taken within two years of the course start date.
7. Waivers may be considered if you have completed a degree (at least 9 months, full-time) taught and assessed entirely in English in a recognised institution, and completed it within two years of the course start date.

3. Imperial College London

1. Requirement: Has two levels: Standard and Higher. Most competitive research programs will require the Higher level.
2. Higher Level IELTS Academic: Overall score of 7.0, with a minimum of 6.5 in all elements.
3. Higher Level TOEFL iBT: Overall score of 100, with a minimum of 22 in each element.
4. Conditions:
5. Scores must be achieved in a single test sitting (IELTS One Skill Retakes are not accepted).
6. The test result must be valid for two years and valid at the beginning of your studies.
7. All doctoral students must also fulfil the Imperial College London Doctoral Academic Communication Requirement (DACR) after meeting the entry requirement.

4. University College London (UCL)

1. Requirement: Has five proficiency levels (Level 1 to Level 5) that vary by department/programme. Most research degrees require Level 3 or Level 4.
2. Level 3 IELTS Academic: Overall score of 7.0, with a minimum of 7.0 in each component.
3. Level 4 IELTS Academic: Overall score of 7.5, with a minimum of 7.0 in each component.
4. Conditions:
5. Test results must be received no more than two years before the proposed date of enrolment.
6. You can be exempted if you have completed at least 12 months of academic education leading to an awarded qualification in a UCL-recognised 'majority English-speaking' country, and the medium of instruction was English.

5. London School of Economics and Political Science (LSE)

1. Requirement: Has three levels: Standard, Higher, and Research (for most MPhil/PhD programs). Law programs have a separate, higher requirement.
2. Research Level IELTS Academic: Overall score of 7.0, with a minimum of 7.0 in Writing, and 6.5 in Reading, Listening, and Speaking.
3. Conditions:
4. English tests must be less than two years old on October 1st in the year you intend to start your programme.
5. You must meet the requirements through a single test sitting.

6. The University of Edinburgh

1. Requirement: Has four categories of English proficiency that vary by school/college. Most PGR programmes require Category B or Category C.
2. Category B IELTS Academic: Overall score of 6.5, with a minimum of 6.0 in each component.
3. Category C IELTS Academic: Overall score of 7.0, with a minimum of 6.5 in each component.
4. Conditions:
5. IELTS and TOEFL tests must be no more than two years old at the start of your programme.
6. Other accepted tests (like Cambridge) may be valid for up to three and a half years.
7. You must meet the requirement in a single test.

7. King's College London (KCL)

1. Requirement: Has three English language levels: Band A, B, and C. Most PGR programmes fall under Band B or C.
2. Band B IELTS Academic: Overall score of 7.0, with a minimum of 6.5 in all four skills.
3. Band C IELTS Academic: Overall score of 7.5, with a minimum of 7.0 in all four skills.
4. Conditions:
5. All test results are generally valid for two years from the date of the examination.
6. Scores must be achieved in one sitting of the test.

8. The University of Manchester

1. Requirement: Requirements vary by course, but generally require high scores for research degrees. Typical minimums for PGR are IELTS 7.0 or 7.5.
2. Example IELTS Academic: Overall score of 7.0, with a minimum of 6.5 in each sub-skill.
3. Conditions:
4. Tests (IELTS, TOEFL, etc.) are valid for two years after the test date.
5. The university does not accept IELTS Online or TOEFL iBT Home Edition for some purposes, so check the course-specific guidance.
6. You must meet the minimum sub-skill scores in a single test.

9. University of Warwick

1. Requirement: Varies, but many PGR programmes require a Band A or Band B.
2. Band A IELTS Academic: Overall score of 6.5, with a maximum of two components at 6.0 and the rest at 6.5 or higher.
3. Band B IELTS Academic: Overall score of 7.0, with a maximum of two components at 6.0 or 6.5 and the rest at 7.0 or higher.
4. Conditions:
5. The test must be taken less than two years before the course start date.
6. Specific departments (e.g., Law, certain MBA/Finance) may have higher individual component scores.

10. University of Bristol

1. Requirement: Has several language profiles (A, B, C, D, E) depending on the faculty/course. Most PGR programs require Profile D or E.
2. Profile D IELTS Academic: Overall score of 6.5, with a minimum of 6.5 in all four skills.
3. Profile E IELTS Academic: Overall score of 7.0, with a minimum of 6.5 in all four skills.
4. Conditions:
5. Test results must have been awarded within two years of the start of your course.
6. An exemption may apply if you've completed an undergraduate or taught master's degree in a majority English-speaking country within the last three years.

Key takeaway: For international postgraduate research scholarships at top UK universities, the common minimum standard is an IELTS Academic overall score of 7.0 with no band below 6.5 or 7.0. Always check the specific course page for the most accurate and up-to-date requirement, as departments may set a higher minimum than the university's general standard.