Hey.
For English, reading the newspaper daily would improve your speed for the reading section. Focus on the Editorial section of newspaper like the hindu etc for this purpose. In case you are looking for a separate book For Vocabulary you can refer the book Word Power Made Easy by Normal Lewis. You will come across various words while reading the newspaper too, prepare a list, go through them regularly and try to use them in sentences. You should read the Editorial section of the Hindu for your Reading section as well as Vocabulary section of CLAT. For the reading section practicing your sample questions while timing it would prove usefull.

For grammar you can use the Wren & Martin.
Practicing questions in practice books or any all inclusive guides like Universal, arihant etc woukd be usefull. If you plan to prepare by coaching from CL, Clat possible, Bulls eye etc then you can refer to their material as it will be sufficient. Along with it go for the newspapers. You won't need to buy separate books.
Best of luck

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