You can use groupby with function size.
Then I reset index with rename column 0 to count.
print df
Month LSOA code Longitude Latitude Crime type
0 2015-01 E01000916 -0.106453 51.518207 Bicycle theft
1 2015-01 E01000914 -0.111497 51.518226 Burglary
2 2015-01 E01000914 -0.111497 51.518226 Burglary
3 2015-01 E01000914 -0.111497 51.518226 Other theft
4 2015-01 E01000914 -0.113767 51.517372 Theft from the person
df = df.groupby(['Longitude', 'Latitude', 'Crime type']).size().reset_index(name="count")
print df
Longitude Latitude Crime type count
0 -0.113767 51.517372 Theft from the person 1
1 -0.111497 51.518226 Burglary 2
2 -0.111497 51.518226 Other theft 1
3 -0.106453 51.518207 Bicycle theft 1
print df['count']
0 1
1 2
2 1
3 1
Name: count, dtype: int64