Oracle 11g Release 2

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

/* Formatted on 1/29/2020 2:59:01 PM (QP5 v5.256.13226.35510) */
WITH MY_TABLE (EMP_ID,
                 DATETIME,
                 CITY,
                 RANK_CITY)
     AS (SELECT 2258325,
                '1/18/2020 5:37',
                'London',
                1
           FROM DUAL
         UNION ALL
         SELECT 2258325,
                '1/19/2020 11:01',
                'Manchester',
                2
           FROM DUAL
         UNION ALL
         SELECT 2258325,
                '1/20/2020 15:06',
                'London',
                3
           FROM DUAL
           
           
                    UNION ALL
         SELECT 2258325,
                '1/21/2020 17:06',
                'London',
                4
           FROM DUAL
           
           
                    UNION ALL
         SELECT 2258325,
                '1/22/2020 12:06',
                'Liverpool',
                5
           FROM DUAL
         UNION ALL
         SELECT 2656700,
                '1/20/2020 23:59',
                'Manchester',
                1
           FROM DUAL
         UNION ALL
         SELECT 2656700,
                '1/21/2020 6:48',
                'London',
                2
           FROM DUAL
         UNION ALL
         SELECT 2656700,
                '1/22/2020 7:40',
                'Liverpool',
                3
           FROM DUAL
         UNION ALL
         SELECT 2656700,
                '1/24/2020 02:40',
                'Manchester',
                4
           FROM DUAL
                    UNION ALL
         SELECT 2656700,
                '1/26/2020 10:47',
                'London',
                5
           FROM DUAL
           
         UNION ALL
         SELECT 6631583,
                '1/18/2020 18:00',
                'London',
                1
           FROM DUAL
         UNION ALL
         SELECT 6631583,
                '1/19/2020 14:25',
                'Manchester',
                2
           FROM DUAL
         UNION ALL
         SELECT 6631583,
                '1/20/2020 8:53',
                'Liverpool',
                3
           FROM DUAL
         UNION ALL
         SELECT 6631583,
                '1/20/2020 14:48',
                'Manchester',
                4
           FROM DUAL
         UNION ALL
         SELECT 6631583,
                '1/21/2020 11:34',
                'London',
                5
           FROM DUAL
         UNION ALL
         SELECT 6631583,
                '1/22/2020 14:48',
                'Manchester',
                6
           FROM DUAL
         UNION ALL
         SELECT 6631583,
                '1/24/2020 11:34',
                'London',
                7
           FROM DUAL)

SELECT * 
FROM (SELECT t.*,
             LEAD(CITY) OVER (PARTITION BY EMP_ID ORDER BY DATETIME) as city_2,
             LEAD(datetime) OVER (PARTITION BY EMP_ID ORDER BY DATETIME) as datetime_2,
             LEAD(CASE WHEN CITY = 'London' THEN CITY END IGNORE NULLS) OVER (PARTITION BY EMP_ID ORDER BY DATETIME) as city_3,
             LEAD(CASE WHEN CITY = 'London' THEN DATETIME END IGNORE NULLS) OVER (PARTITION BY EMP_ID ORDER BY DATETIME) as datetime_3
      FROM MY_TABLE t
     ) t
 WHERE CITY = 'London' AND CITY_2 <> 'London' AND CITY_3 = 'London'

EMP_ID	DATETIME	CITY	RANK_CITY	CITY_2	DATETIME_2	CITY_3	DATETIME_3
2258325	1/18/2020 5:37	London	1	Manchester	1/19/2020 11:01	London	1/20/2020 15:06
2656700	1/21/2020 6:48	London	2	Liverpool	1/22/2020 7:40	London	1/26/2020 10:47
6631583	1/18/2020 18:00	London	1	Manchester	1/19/2020 14:25	London	1/21/2020 11:34
6631583	1/21/2020 11:34	London	5	Manchester	1/22/2020 14:48	London	1/24/2020 11:34